What is the difference between antiderivative and derivative?
$begingroup$
I am in calculus class right now and I have no idea. I'm sorry for my ignorance.
calculus
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
$endgroup$
add a comment |
$begingroup$
I am in calculus class right now and I have no idea. I'm sorry for my ignorance.
calculus
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
$endgroup$
1
$begingroup$
Don't feel sorry about your ignorance, just be confident and learn. It is not a big deal to not knowing something, you can always learn. Remember things takes time. All the best.
$endgroup$
– Kushal Bhuyan
Dec 14 '15 at 13:20
$begingroup$
Antiderivative is going in the opposite direction. Since the derivative of $3x^3-4$ is $9x^2$, we conclude that an antiderivative of $9x^2$ is $3x^3-4$. I said "an" antiderivative, because there are many of them.
$endgroup$
– GEdgar
Dec 14 '15 at 13:36
add a comment |
$begingroup$
I am in calculus class right now and I have no idea. I'm sorry for my ignorance.
calculus
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
$endgroup$
I am in calculus class right now and I have no idea. I'm sorry for my ignorance.
calculus
calculus
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
asked Dec 14 '15 at 13:10
MelissaMelissa
3815
3815
1
$begingroup$
Don't feel sorry about your ignorance, just be confident and learn. It is not a big deal to not knowing something, you can always learn. Remember things takes time. All the best.
$endgroup$
– Kushal Bhuyan
Dec 14 '15 at 13:20
$begingroup$
Antiderivative is going in the opposite direction. Since the derivative of $3x^3-4$ is $9x^2$, we conclude that an antiderivative of $9x^2$ is $3x^3-4$. I said "an" antiderivative, because there are many of them.
$endgroup$
– GEdgar
Dec 14 '15 at 13:36
add a comment |
1
$begingroup$
Don't feel sorry about your ignorance, just be confident and learn. It is not a big deal to not knowing something, you can always learn. Remember things takes time. All the best.
$endgroup$
– Kushal Bhuyan
Dec 14 '15 at 13:20
$begingroup$
Antiderivative is going in the opposite direction. Since the derivative of $3x^3-4$ is $9x^2$, we conclude that an antiderivative of $9x^2$ is $3x^3-4$. I said "an" antiderivative, because there are many of them.
$endgroup$
– GEdgar
Dec 14 '15 at 13:36
1
1
$begingroup$
Don't feel sorry about your ignorance, just be confident and learn. It is not a big deal to not knowing something, you can always learn. Remember things takes time. All the best.
$endgroup$
– Kushal Bhuyan
Dec 14 '15 at 13:20
$begingroup$
Don't feel sorry about your ignorance, just be confident and learn. It is not a big deal to not knowing something, you can always learn. Remember things takes time. All the best.
$endgroup$
– Kushal Bhuyan
Dec 14 '15 at 13:20
$begingroup$
Antiderivative is going in the opposite direction. Since the derivative of $3x^3-4$ is $9x^2$, we conclude that an antiderivative of $9x^2$ is $3x^3-4$. I said "an" antiderivative, because there are many of them.
$endgroup$
– GEdgar
Dec 14 '15 at 13:36
$begingroup$
Antiderivative is going in the opposite direction. Since the derivative of $3x^3-4$ is $9x^2$, we conclude that an antiderivative of $9x^2$ is $3x^3-4$. I said "an" antiderivative, because there are many of them.
$endgroup$
– GEdgar
Dec 14 '15 at 13:36
add a comment |
5 Answers
5
active
oldest
votes
$begingroup$
The derivative can be defined as the slope of a tangent line. When taking a derivative the general formula to follow would be:
- Constant Rule $frac{d(c)}{dx}=0$
The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. In other words, it is the opposite of a derivative.
It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems
Example: The antiderivative of $sec^2x = tan x + C$
It is also important to remember, when taking the antiderivative, not to forget to add your constant!
edited Dec 14 '15 at 13:33
zz20s
5,26441936
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
$endgroup$
add a comment |
$begingroup$
The anti-derivative of a function, denoted by
$$int f(x)dx$$
yields a function that when differentiated, gives back $f(x)$, while differentiating denoted by
$$frac{d}{dx}f(x)$$
yields a function for the slope of the tangent line at any given $x$ which youre probably used to by now.
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
$endgroup$
add a comment |
$begingroup$
There is not only a difference between antiderivative but also a relation ship. Antiderivative is a "sort of inversve of the derivative" (note, this is not really true, just a somewhat intuitive description, which is the reason for quotations) in the sense of if $f=F'$ then $f$ is derivative of $F$ and $F$ is antiderivative of $f$. Antiderivative is often denoted as an integral, i.e. $F=int f$ but there is examples of $int f(x)dx = L$ where no $F(x)$ exists, for example see this link.
edited Apr 13 '17 at 12:21
Community♦
1
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
$endgroup$
add a comment |
$begingroup$
Anti derivative is integration indefinite integration gives any equation relating $x,y$ while definite integration is area under the given curve while derivatives is finding the slope of given curve . Thats what the basic difference and definitions are. But i would also like to tell you never forget to write $+c$(constant) when you have found out the integration result as its very important. You will get it as you proceed further in calculus
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
$endgroup$
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
add a comment |
$begingroup$
Derivative is rate of change and it can also find the slope as well, in it you can find the piece wise change, while anti-derivative is synonimus to intergration which is inverse of derivatives, it is sometimes used to find the area under the curve, also to find the length of the curve $y=f(x)$
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
$endgroup$
add a comment |
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5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The derivative can be defined as the slope of a tangent line. When taking a derivative the general formula to follow would be:
- Constant Rule $frac{d(c)}{dx}=0$
The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. In other words, it is the opposite of a derivative.
It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems
Example: The antiderivative of $sec^2x = tan x + C$
It is also important to remember, when taking the antiderivative, not to forget to add your constant!
edited Dec 14 '15 at 13:33
zz20s
5,26441936
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
$endgroup$
add a comment |
$begingroup$
The derivative can be defined as the slope of a tangent line. When taking a derivative the general formula to follow would be:
- Constant Rule $frac{d(c)}{dx}=0$
The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. In other words, it is the opposite of a derivative.
It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems
Example: The antiderivative of $sec^2x = tan x + C$
It is also important to remember, when taking the antiderivative, not to forget to add your constant!
edited Dec 14 '15 at 13:33
zz20s
5,26441936
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
$endgroup$
add a comment |
$begingroup$
The derivative can be defined as the slope of a tangent line. When taking a derivative the general formula to follow would be:
- Constant Rule $frac{d(c)}{dx}=0$
The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. In other words, it is the opposite of a derivative.
It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems
Example: The antiderivative of $sec^2x = tan x + C$
It is also important to remember, when taking the antiderivative, not to forget to add your constant!
edited Dec 14 '15 at 13:33
zz20s
5,26441936
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
$endgroup$
The derivative can be defined as the slope of a tangent line. When taking a derivative the general formula to follow would be:
- Constant Rule $frac{d(c)}{dx}=0$
The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. In other words, it is the opposite of a derivative.
It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems
Example: The antiderivative of $sec^2x = tan x + C$
It is also important to remember, when taking the antiderivative, not to forget to add your constant!
edited Dec 14 '15 at 13:33
zz20s
5,26441936
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
edited Dec 14 '15 at 13:33
zz20s
5,26441936
edited Dec 14 '15 at 13:33
zz20s
5,26441936
edited Dec 14 '15 at 13:33
zz20s
5,26441936
5,26441936
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
answered Dec 14 '15 at 13:16
Paula B.Paula B.
1414
1414
add a comment |
add a comment |
$begingroup$
The anti-derivative of a function, denoted by
$$int f(x)dx$$
yields a function that when differentiated, gives back $f(x)$, while differentiating denoted by
$$frac{d}{dx}f(x)$$
yields a function for the slope of the tangent line at any given $x$ which youre probably used to by now.
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
$endgroup$
add a comment |
$begingroup$
The anti-derivative of a function, denoted by
$$int f(x)dx$$
yields a function that when differentiated, gives back $f(x)$, while differentiating denoted by
$$frac{d}{dx}f(x)$$
yields a function for the slope of the tangent line at any given $x$ which youre probably used to by now.
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
$endgroup$
add a comment |
$begingroup$
The anti-derivative of a function, denoted by
$$int f(x)dx$$
yields a function that when differentiated, gives back $f(x)$, while differentiating denoted by
$$frac{d}{dx}f(x)$$
yields a function for the slope of the tangent line at any given $x$ which youre probably used to by now.
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
$endgroup$
The anti-derivative of a function, denoted by
$$int f(x)dx$$
yields a function that when differentiated, gives back $f(x)$, while differentiating denoted by
$$frac{d}{dx}f(x)$$
yields a function for the slope of the tangent line at any given $x$ which youre probably used to by now.
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
answered Dec 14 '15 at 13:18
Will FisherWill Fisher
4,02811132
4,02811132
add a comment |
add a comment |
$begingroup$
There is not only a difference between antiderivative but also a relation ship. Antiderivative is a "sort of inversve of the derivative" (note, this is not really true, just a somewhat intuitive description, which is the reason for quotations) in the sense of if $f=F'$ then $f$ is derivative of $F$ and $F$ is antiderivative of $f$. Antiderivative is often denoted as an integral, i.e. $F=int f$ but there is examples of $int f(x)dx = L$ where no $F(x)$ exists, for example see this link.
edited Apr 13 '17 at 12:21
Community♦
1
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
$endgroup$
add a comment |
$begingroup$
There is not only a difference between antiderivative but also a relation ship. Antiderivative is a "sort of inversve of the derivative" (note, this is not really true, just a somewhat intuitive description, which is the reason for quotations) in the sense of if $f=F'$ then $f$ is derivative of $F$ and $F$ is antiderivative of $f$. Antiderivative is often denoted as an integral, i.e. $F=int f$ but there is examples of $int f(x)dx = L$ where no $F(x)$ exists, for example see this link.
edited Apr 13 '17 at 12:21
Community♦
1
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
$endgroup$
add a comment |
$begingroup$
There is not only a difference between antiderivative but also a relation ship. Antiderivative is a "sort of inversve of the derivative" (note, this is not really true, just a somewhat intuitive description, which is the reason for quotations) in the sense of if $f=F'$ then $f$ is derivative of $F$ and $F$ is antiderivative of $f$. Antiderivative is often denoted as an integral, i.e. $F=int f$ but there is examples of $int f(x)dx = L$ where no $F(x)$ exists, for example see this link.
edited Apr 13 '17 at 12:21
Community♦
1
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
$endgroup$
There is not only a difference between antiderivative but also a relation ship. Antiderivative is a "sort of inversve of the derivative" (note, this is not really true, just a somewhat intuitive description, which is the reason for quotations) in the sense of if $f=F'$ then $f$ is derivative of $F$ and $F$ is antiderivative of $f$. Antiderivative is often denoted as an integral, i.e. $F=int f$ but there is examples of $int f(x)dx = L$ where no $F(x)$ exists, for example see this link.
edited Apr 13 '17 at 12:21
Community♦
1
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
1
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
answered Dec 14 '15 at 13:20
Michael MedvinskyMichael Medvinsky
5,37031131
5,37031131
add a comment |
add a comment |
$begingroup$
Anti derivative is integration indefinite integration gives any equation relating $x,y$ while definite integration is area under the given curve while derivatives is finding the slope of given curve . Thats what the basic difference and definitions are. But i would also like to tell you never forget to write $+c$(constant) when you have found out the integration result as its very important. You will get it as you proceed further in calculus
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
$endgroup$
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
add a comment |
$begingroup$
Anti derivative is integration indefinite integration gives any equation relating $x,y$ while definite integration is area under the given curve while derivatives is finding the slope of given curve . Thats what the basic difference and definitions are. But i would also like to tell you never forget to write $+c$(constant) when you have found out the integration result as its very important. You will get it as you proceed further in calculus
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
$endgroup$
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
add a comment |
$begingroup$
Anti derivative is integration indefinite integration gives any equation relating $x,y$ while definite integration is area under the given curve while derivatives is finding the slope of given curve . Thats what the basic difference and definitions are. But i would also like to tell you never forget to write $+c$(constant) when you have found out the integration result as its very important. You will get it as you proceed further in calculus
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
$endgroup$
Anti derivative is integration indefinite integration gives any equation relating $x,y$ while definite integration is area under the given curve while derivatives is finding the slope of given curve . Thats what the basic difference and definitions are. But i would also like to tell you never forget to write $+c$(constant) when you have found out the integration result as its very important. You will get it as you proceed further in calculus
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
edited Dec 14 '15 at 13:23
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
answered Dec 14 '15 at 13:14
Archis WelankarArchis Welankar
12.1k41642
12.1k41642
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
add a comment |
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
$begingroup$
Anti-differentiation produces the function that describes the area under the curve. Definite integration is used to compute the area.
$endgroup$
– Alvin Lepik
Dec 14 '15 at 13:18
add a comment |
$begingroup$
Derivative is rate of change and it can also find the slope as well, in it you can find the piece wise change, while anti-derivative is synonimus to intergration which is inverse of derivatives, it is sometimes used to find the area under the curve, also to find the length of the curve $y=f(x)$
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
$endgroup$
add a comment |
$begingroup$
Derivative is rate of change and it can also find the slope as well, in it you can find the piece wise change, while anti-derivative is synonimus to intergration which is inverse of derivatives, it is sometimes used to find the area under the curve, also to find the length of the curve $y=f(x)$
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
$endgroup$
add a comment |
$begingroup$
Derivative is rate of change and it can also find the slope as well, in it you can find the piece wise change, while anti-derivative is synonimus to intergration which is inverse of derivatives, it is sometimes used to find the area under the curve, also to find the length of the curve $y=f(x)$
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
$endgroup$
Derivative is rate of change and it can also find the slope as well, in it you can find the piece wise change, while anti-derivative is synonimus to intergration which is inverse of derivatives, it is sometimes used to find the area under the curve, also to find the length of the curve $y=f(x)$
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
edited Dec 23 '18 at 17:45
Maria Mazur
49.5k1361124
49.5k1361124
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
answered Dec 23 '18 at 17:26
Amjad iqbalAmjad iqbal
1
1
add a comment |
add a comment |
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$begingroup$
Don't feel sorry about your ignorance, just be confident and learn. It is not a big deal to not knowing something, you can always learn. Remember things takes time. All the best.
$endgroup$
– Kushal Bhuyan
Dec 14 '15 at 13:20
$begingroup$
Antiderivative is going in the opposite direction. Since the derivative of $3x^3-4$ is $9x^2$, we conclude that an antiderivative of $9x^2$ is $3x^3-4$. I said "an" antiderivative, because there are many of them.
$endgroup$
– GEdgar
Dec 14 '15 at 13:36