Derivative of $ log _{2} (log_{3}(log_{5}b)) $ [closed]
I am supposed to find the derivative of $f(b)= log _{2} (log_{3}(log_{5}b)) $ How would you calculate it? I know rules for derivation of logarithms but I don't know how to apply it in this case. Thanks
derivatives
asked Nov 24 at 20:48
Johny547
1154
closed as off-topic by Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF Dec 3 at 5:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
I am supposed to find the derivative of $f(b)= log _{2} (log_{3}(log_{5}b)) $ How would you calculate it? I know rules for derivation of logarithms but I don't know how to apply it in this case. Thanks
derivatives
asked Nov 24 at 20:48
Johny547
1154
closed as off-topic by Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF Dec 3 at 5:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF
If this question can be reworded to fit the rules in the help center, please edit the question.
2
First you can tidy up a little bit using the rule $log_a(b)=frac{log(b)}{log(a)}$.
– Nodt Greenish
Nov 24 at 20:54
What have you tried? Where are you getting stuck? Do you know the chain rule?
– DRF
Dec 3 at 5:56
add a comment |
I am supposed to find the derivative of $f(b)= log _{2} (log_{3}(log_{5}b)) $ How would you calculate it? I know rules for derivation of logarithms but I don't know how to apply it in this case. Thanks
derivatives
asked Nov 24 at 20:48
Johny547
1154
I am supposed to find the derivative of $f(b)= log _{2} (log_{3}(log_{5}b)) $ How would you calculate it? I know rules for derivation of logarithms but I don't know how to apply it in this case. Thanks
derivatives
derivatives
asked Nov 24 at 20:48
Johny547
1154
asked Nov 24 at 20:48
Johny547
1154
edited Nov 24 at 20:54
asked Nov 24 at 20:48
Johny547
1154
asked Nov 24 at 20:48
Johny547
1154
asked Nov 24 at 20:48
Johny547
1154
1154
closed as off-topic by Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF Dec 3 at 5:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF Dec 3 at 5:57
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Did, Saad, Jyrki Lahtonen, Brahadeesh, DRF
If this question can be reworded to fit the rules in the help center, please edit the question.
2
First you can tidy up a little bit using the rule $log_a(b)=frac{log(b)}{log(a)}$.
– Nodt Greenish
Nov 24 at 20:54
What have you tried? Where are you getting stuck? Do you know the chain rule?
– DRF
Dec 3 at 5:56
add a comment |
2
First you can tidy up a little bit using the rule $log_a(b)=frac{log(b)}{log(a)}$.
– Nodt Greenish
Nov 24 at 20:54
What have you tried? Where are you getting stuck? Do you know the chain rule?
– DRF
Dec 3 at 5:56
2
2
First you can tidy up a little bit using the rule $log_a(b)=frac{log(b)}{log(a)}$.
– Nodt Greenish
Nov 24 at 20:54
First you can tidy up a little bit using the rule $log_a(b)=frac{log(b)}{log(a)}$.
– Nodt Greenish
Nov 24 at 20:54
What have you tried? Where are you getting stuck? Do you know the chain rule?
– DRF
Dec 3 at 5:56
What have you tried? Where are you getting stuck? Do you know the chain rule?
– DRF
Dec 3 at 5:56
add a comment |
1 Answer
1
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oldest
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$f(x)=log_2(log_3(log_5(x)))$, find $f'(x)|_{x=b}$
Chain rule: $(f(g(x)))'=f'(g(x))g'(x)$
and
$(log_a x)'=left(cfrac {ln x}{ln a}right)'=cfrac 1{xln a }$
Apply above rule:
begin{align}
f'(x)&=cfrac 1{ln 2 log_3(log_5(x))}cdot (log_3(log_5(x)))'\
&=cfrac 1{ln 2 ln 3 log_3(log_5(x))log_5(x)}cdot (log_5(x))'\
&=cfrac 1{ln 2 cdot ln 3 cdot ln 5log_3(log_5(x))cdot log_5(x) cdot x}
end{align}
Replace $x$ with $b$ to get $f'(b)$
answered Nov 24 at 21:08
Lance
54229
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$f(x)=log_2(log_3(log_5(x)))$, find $f'(x)|_{x=b}$
Chain rule: $(f(g(x)))'=f'(g(x))g'(x)$
and
$(log_a x)'=left(cfrac {ln x}{ln a}right)'=cfrac 1{xln a }$
Apply above rule:
begin{align}
f'(x)&=cfrac 1{ln 2 log_3(log_5(x))}cdot (log_3(log_5(x)))'\
&=cfrac 1{ln 2 ln 3 log_3(log_5(x))log_5(x)}cdot (log_5(x))'\
&=cfrac 1{ln 2 cdot ln 3 cdot ln 5log_3(log_5(x))cdot log_5(x) cdot x}
end{align}
Replace $x$ with $b$ to get $f'(b)$
answered Nov 24 at 21:08
Lance
54229
add a comment |
$f(x)=log_2(log_3(log_5(x)))$, find $f'(x)|_{x=b}$
Chain rule: $(f(g(x)))'=f'(g(x))g'(x)$
and
$(log_a x)'=left(cfrac {ln x}{ln a}right)'=cfrac 1{xln a }$
Apply above rule:
begin{align}
f'(x)&=cfrac 1{ln 2 log_3(log_5(x))}cdot (log_3(log_5(x)))'\
&=cfrac 1{ln 2 ln 3 log_3(log_5(x))log_5(x)}cdot (log_5(x))'\
&=cfrac 1{ln 2 cdot ln 3 cdot ln 5log_3(log_5(x))cdot log_5(x) cdot x}
end{align}
Replace $x$ with $b$ to get $f'(b)$
answered Nov 24 at 21:08
Lance
54229
add a comment |
$f(x)=log_2(log_3(log_5(x)))$, find $f'(x)|_{x=b}$
Chain rule: $(f(g(x)))'=f'(g(x))g'(x)$
and
$(log_a x)'=left(cfrac {ln x}{ln a}right)'=cfrac 1{xln a }$
Apply above rule:
begin{align}
f'(x)&=cfrac 1{ln 2 log_3(log_5(x))}cdot (log_3(log_5(x)))'\
&=cfrac 1{ln 2 ln 3 log_3(log_5(x))log_5(x)}cdot (log_5(x))'\
&=cfrac 1{ln 2 cdot ln 3 cdot ln 5log_3(log_5(x))cdot log_5(x) cdot x}
end{align}
Replace $x$ with $b$ to get $f'(b)$
answered Nov 24 at 21:08
Lance
54229
$f(x)=log_2(log_3(log_5(x)))$, find $f'(x)|_{x=b}$
Chain rule: $(f(g(x)))'=f'(g(x))g'(x)$
and
$(log_a x)'=left(cfrac {ln x}{ln a}right)'=cfrac 1{xln a }$
Apply above rule:
begin{align}
f'(x)&=cfrac 1{ln 2 log_3(log_5(x))}cdot (log_3(log_5(x)))'\
&=cfrac 1{ln 2 ln 3 log_3(log_5(x))log_5(x)}cdot (log_5(x))'\
&=cfrac 1{ln 2 cdot ln 3 cdot ln 5log_3(log_5(x))cdot log_5(x) cdot x}
end{align}
Replace $x$ with $b$ to get $f'(b)$
answered Nov 24 at 21:08
Lance
54229
answered Nov 24 at 21:08
Lance
54229
answered Nov 24 at 21:08
Lance
54229
answered Nov 24 at 21:08
Lance
54229
54229
add a comment |
add a comment |
2
First you can tidy up a little bit using the rule $log_a(b)=frac{log(b)}{log(a)}$.
– Nodt Greenish
Nov 24 at 20:54
What have you tried? Where are you getting stuck? Do you know the chain rule?
– DRF
Dec 3 at 5:56