What is derivative of $sin ax$ where $a$ is a constant?












1














What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question




















  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 '18 at 15:17
















1














What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question




















  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 '18 at 15:17














1












1








1







What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential







share|cite|improve this question















What is the derivative of $sin a x$ where $a$ is a constant.




Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.



I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $sin ax $ or $cos ax$. Whatever..
Please help me get my concept clear.




Thank You!






calculus algebra-precalculus derivatives differential




calculus algebra-precalculus derivatives differential






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 29 '18 at 19:19









Asaf Karagila♦

302k32427757




302k32427757










asked Nov 29 '18 at 15:17









Chaku DakuChaku Daku

91




91








  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 '18 at 15:17














  • 1




    Apply the chain rule.
    – user3482749
    Nov 29 '18 at 15:17








1




1




Apply the chain rule.
– user3482749
Nov 29 '18 at 15:17




Apply the chain rule.
– user3482749
Nov 29 '18 at 15:17










3 Answers
3






active

oldest

votes


















6














HINT



Recall that by chain rule



$$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






share|cite|improve this answer





























    3














    begin{array}{c}
    frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
    = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
    = left( {cos ax} right) cdot a cdot 1\
    = aleft( {cos ax} right)
    end{array}






    share|cite|improve this answer

















    • 1




      Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
      – Chris
      Nov 29 '18 at 17:20






    • 1




      @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
      – Paul Sinclair
      Nov 29 '18 at 17:29



















    1














    Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






    share|cite|improve this answer























      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3018756%2fwhat-is-derivative-of-sin-ax-where-a-is-a-constant%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      6














      HINT



      Recall that by chain rule



      $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






      share|cite|improve this answer


























        6














        HINT



        Recall that by chain rule



        $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






        share|cite|improve this answer
























          6












          6








          6






          HINT



          Recall that by chain rule



          $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$






          share|cite|improve this answer












          HINT



          Recall that by chain rule



          $$frac{d}{dx}[sin (f(x))]=cos (f(x))cdot f'(x)$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 29 '18 at 15:20









          gimusigimusi

          1




          1























              3














              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer

















              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 '18 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 '18 at 17:29
















              3














              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer

















              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 '18 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 '18 at 17:29














              3












              3








              3






              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}






              share|cite|improve this answer












              begin{array}{c}
              frac{d}{{dx}}left( {sin ax} right) = left( {cos ax} right)frac{d}{{dx}}left( {ax} right)\
              = left( {cos ax} right) cdot a cdot frac{{dx}}{{dx}}\
              = left( {cos ax} right) cdot a cdot 1\
              = aleft( {cos ax} right)
              end{array}







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Nov 29 '18 at 16:10









              Krishna SrivastavKrishna Srivastav

              894




              894








              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 '18 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 '18 at 17:29














              • 1




                Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
                – Chris
                Nov 29 '18 at 17:20






              • 1




                @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
                – Paul Sinclair
                Nov 29 '18 at 17:29








              1




              1




              Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
              – Chris
              Nov 29 '18 at 17:20




              Out of interest why can you not just go straight from the first line to the last line without needing to have the $dx/dx$ part in there too?
              – Chris
              Nov 29 '18 at 17:20




              1




              1




              @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
              – Paul Sinclair
              Nov 29 '18 at 17:29




              @Chris - because going straight from the first line to the last is simply skipping over steps that are required by a direct application of the theorems, but are so trivial people usually don't bother to write them down. Krishna Srivastav has simply chosen to show all the steps to make it clear how the full calculation proceeds. Occasionally a good teacher has to do this, as what makes those steps trivial is that everyone understands them. However, this is not always true of new students.
              – Paul Sinclair
              Nov 29 '18 at 17:29











              1














              Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






              share|cite|improve this answer




























                1














                Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






                share|cite|improve this answer


























                  1












                  1








                  1






                  Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.






                  share|cite|improve this answer














                  Derivative of $sin(ax) = a cos(ax)$ by Chain Rule.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Nov 29 '18 at 15:42









                  Tianlalu

                  3,09621038




                  3,09621038










                  answered Nov 29 '18 at 15:21









                  Rohit BharadwajRohit Bharadwaj

                  518




                  518






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.





                      Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                      Please pay close attention to the following guidance:


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3018756%2fwhat-is-derivative-of-sin-ax-where-a-is-a-constant%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Le Mesnil-Réaume

                      Image
                      Le Mesnil-Réaume Region Normandie Département Seine-Maritime Arrondissement Dieppe Kanton Eu Gemeindeverband Villes Sœurs Koordinaten 49° 58′  N , 1° 27′  O 49.9725 1.4463888888889 Koordinaten: 49° 58′  N , 1° 27′  O Höhe 92–156 m Fläche 5,55 km 2 Einwohner 793 (1. Januar 2016) Bevölkerungsdichte 143 Einw./km 2 Postleitzahl 76260 INSEE-Code 76435 Website http://www.mesnil-reaume.net/ Rathaus (Mairie) und Schule von Le Mesnil-Réaume Le Mesnil-Réaume ist eine französische Gemeinde mit 793 Einwohnern (Stand: 1. Januar 2016) im Département Seine-Maritime in der Region Normandie (vor 2016 Haute-Normandie). Sie gehört zum Arrondissement Dieppe und zum Kanton Eu. Die Einwohner werden Mesnillais genannt. Inhaltsverzeichnis 1 Geographie 2 Bevölkerungsentwicklung 3 Sehenswürdigkeiten 4 Weblinks Geographie | Le Mesnil-Réaume liegt etwa 43 Kilomet
                      Read more

                      Ida-Boy-Ed-Garten

                      Image
                      Die Lage des Ida-Boy-Ed-Gartens, rot markiert Der Ida-Boy-Ed-Garten Der Ida-Boy-Ed-Garten, Blick von der Wakenitzmauer durch das Tor in der Stadtmauer Der Ida-Boy-Ed-Garten ist eine Straße der Lübecker Altstadt. Inhaltsverzeichnis 1 Lage 2 Geschichte 3 Literatur 4 Weblinks Lage | Der etwa 90 Meter lange Ida-Boy-Ed-Garten befindet sich an der nördlichen Spitze der Altstadtinsel, vor dem Burgtor. Die in einem Bogen durch eine Grünanlage hangaufwärts führende Straße verbindet die Wakenitzmauer mit der Burgtorbrücke. Geschichte | Der heutige Ida-Boy-Ed-Garten wurde ursprünglich als Verlängerung der Wakenitzmauer angelegt. 1903 wurde in den erhaltenen Teil der mittelalterlichen Stadtmauer, an dem die Wakenitzmauer bei der Einmündung der Kaiserstraße begann, ein Tor mit einem großen Bogen für die Durchführung der Straße und zwei kleineren seitlichen Öffnungen für Fußgänger gebrochen, um für die neu errichteten Wohnhäuser in diesem Bereich
                      Read more

                      web3.py web3.isConnected() returns false always

                      Image
                      1 I am trying an tutorial on web3.py so i created a profile in infura and used its project id.But it shows false always when i try web3.isConnected() PS C:UsersHP> python Python 3.6.3 (v3.6.3:2c5fed8, Oct 3 2017, 18:11:49) [MSC v.1900 64 bit (AMD64)] on win32 Type "help", "copyright", "credits" or "license" for more information. >>> from web3 import Web3 >>> infura_url = "mainnet.infura.io/v3/******************************" >>> web3 = Web3(Web3.HTTPProvider(infura_url)) >>> web3.isConnected() False web3.py share | improve this question
                      Read more