First derivative on 2 variables [closed]
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I got a problem that is causing me a headache. So differentiating $frac {1}{12π}*c^2*h$.
According to the constant rule we can pull out the constant $frac {1}{12π}$ and differenciate $c^2*h$ as two different variables using the chain rule along with the product rule? The problem here is that my solutions doesn't match the online calculators which are taking $c^2$ as a constant and therefore produce the following answer $c cdot frac {h}{6π}$. I don't understant what I'm I doing wrong
derivatives
edited Nov 18 at 0:16
bjcolby15
1,0941916
asked Nov 18 at 0:01
David
61
closed as unclear what you're asking by Scientifica, Lord Shark the Unknown, max_zorn, Brahadeesh, Rebellos Nov 18 at 11:57
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
1
down vote
favorite
I got a problem that is causing me a headache. So differentiating $frac {1}{12π}*c^2*h$.
According to the constant rule we can pull out the constant $frac {1}{12π}$ and differenciate $c^2*h$ as two different variables using the chain rule along with the product rule? The problem here is that my solutions doesn't match the online calculators which are taking $c^2$ as a constant and therefore produce the following answer $c cdot frac {h}{6π}$. I don't understant what I'm I doing wrong
derivatives
edited Nov 18 at 0:16
bjcolby15
1,0941916
asked Nov 18 at 0:01
David
61
closed as unclear what you're asking by Scientifica, Lord Shark the Unknown, max_zorn, Brahadeesh, Rebellos Nov 18 at 11:57
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
differentiating with respect to what?
– valer
Nov 18 at 0:02
With respect to time (t) so V=volume, (d/d(t)V= d/d(t)(1/12π)*c^2*h
– David
Nov 18 at 0:09
in that case $c$ or $h$ (at least one of them) must be a function of $t$ or else the answer is $0$.
– valer
Nov 18 at 0:13
If you prob write c(t) instead of c, then the online calculators should work (and of course h(t) instead of h)
– Stan Tendijck
Nov 18 at 0:54
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I got a problem that is causing me a headache. So differentiating $frac {1}{12π}*c^2*h$.
According to the constant rule we can pull out the constant $frac {1}{12π}$ and differenciate $c^2*h$ as two different variables using the chain rule along with the product rule? The problem here is that my solutions doesn't match the online calculators which are taking $c^2$ as a constant and therefore produce the following answer $c cdot frac {h}{6π}$. I don't understant what I'm I doing wrong
derivatives
edited Nov 18 at 0:16
bjcolby15
1,0941916
asked Nov 18 at 0:01
David
61
I got a problem that is causing me a headache. So differentiating $frac {1}{12π}*c^2*h$.
According to the constant rule we can pull out the constant $frac {1}{12π}$ and differenciate $c^2*h$ as two different variables using the chain rule along with the product rule? The problem here is that my solutions doesn't match the online calculators which are taking $c^2$ as a constant and therefore produce the following answer $c cdot frac {h}{6π}$. I don't understant what I'm I doing wrong
derivatives
derivatives
edited Nov 18 at 0:16
bjcolby15
1,0941916
asked Nov 18 at 0:01
David
61
edited Nov 18 at 0:16
bjcolby15
1,0941916
asked Nov 18 at 0:01
David
61
edited Nov 18 at 0:16
bjcolby15
1,0941916
edited Nov 18 at 0:16
bjcolby15
1,0941916
edited Nov 18 at 0:16
bjcolby15
1,0941916
1,0941916
asked Nov 18 at 0:01
David
61
asked Nov 18 at 0:01
David
61
asked Nov 18 at 0:01
David
61
61
closed as unclear what you're asking by Scientifica, Lord Shark the Unknown, max_zorn, Brahadeesh, Rebellos Nov 18 at 11:57
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Scientifica, Lord Shark the Unknown, max_zorn, Brahadeesh, Rebellos Nov 18 at 11:57
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
2
differentiating with respect to what?
– valer
Nov 18 at 0:02
With respect to time (t) so V=volume, (d/d(t)V= d/d(t)(1/12π)*c^2*h
– David
Nov 18 at 0:09
in that case $c$ or $h$ (at least one of them) must be a function of $t$ or else the answer is $0$.
– valer
Nov 18 at 0:13
If you prob write c(t) instead of c, then the online calculators should work (and of course h(t) instead of h)
– Stan Tendijck
Nov 18 at 0:54
add a comment |
2
differentiating with respect to what?
– valer
Nov 18 at 0:02
With respect to time (t) so V=volume, (d/d(t)V= d/d(t)(1/12π)*c^2*h
– David
Nov 18 at 0:09
in that case $c$ or $h$ (at least one of them) must be a function of $t$ or else the answer is $0$.
– valer
Nov 18 at 0:13
If you prob write c(t) instead of c, then the online calculators should work (and of course h(t) instead of h)
– Stan Tendijck
Nov 18 at 0:54
2
2
differentiating with respect to what?
– valer
Nov 18 at 0:02
differentiating with respect to what?
– valer
Nov 18 at 0:02
With respect to time (t) so V=volume, (d/d(t)V= d/d(t)(1/12π)*c^2*h
– David
Nov 18 at 0:09
With respect to time (t) so V=volume, (d/d(t)V= d/d(t)(1/12π)*c^2*h
– David
Nov 18 at 0:09
in that case $c$ or $h$ (at least one of them) must be a function of $t$ or else the answer is $0$.
– valer
Nov 18 at 0:13
in that case $c$ or $h$ (at least one of them) must be a function of $t$ or else the answer is $0$.
– valer
Nov 18 at 0:13
If you prob write c(t) instead of c, then the online calculators should work (and of course h(t) instead of h)
– Stan Tendijck
Nov 18 at 0:54
If you prob write c(t) instead of c, then the online calculators should work (and of course h(t) instead of h)
– Stan Tendijck
Nov 18 at 0:54
add a comment |
1 Answer
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1
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In the most general case, both $c$ and $h$ are functions of $t$. Then you can write:
$frac{dV(t)}{dt}$
= $ frac{1}{12 pi}frac{d}{dt}c^2(t)h(t)$
= $frac{1}{12 pi} left( 2c(t)c'(t)h(t) + c^2(t)h'(t)right)$.
That's as far as one can get until you tell us how $c$ and $h$ vary as functions of $t$.
answered Nov 18 at 3:19
Aditya Dua
5958
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
In the most general case, both $c$ and $h$ are functions of $t$. Then you can write:
$frac{dV(t)}{dt}$
= $ frac{1}{12 pi}frac{d}{dt}c^2(t)h(t)$
= $frac{1}{12 pi} left( 2c(t)c'(t)h(t) + c^2(t)h'(t)right)$.
That's as far as one can get until you tell us how $c$ and $h$ vary as functions of $t$.
answered Nov 18 at 3:19
Aditya Dua
5958
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
add a comment |
up vote
1
down vote
In the most general case, both $c$ and $h$ are functions of $t$. Then you can write:
$frac{dV(t)}{dt}$
= $ frac{1}{12 pi}frac{d}{dt}c^2(t)h(t)$
= $frac{1}{12 pi} left( 2c(t)c'(t)h(t) + c^2(t)h'(t)right)$.
That's as far as one can get until you tell us how $c$ and $h$ vary as functions of $t$.
answered Nov 18 at 3:19
Aditya Dua
5958
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
add a comment |
up vote
1
down vote
up vote
1
down vote
In the most general case, both $c$ and $h$ are functions of $t$. Then you can write:
$frac{dV(t)}{dt}$
= $ frac{1}{12 pi}frac{d}{dt}c^2(t)h(t)$
= $frac{1}{12 pi} left( 2c(t)c'(t)h(t) + c^2(t)h'(t)right)$.
That's as far as one can get until you tell us how $c$ and $h$ vary as functions of $t$.
answered Nov 18 at 3:19
Aditya Dua
5958
In the most general case, both $c$ and $h$ are functions of $t$. Then you can write:
$frac{dV(t)}{dt}$
= $ frac{1}{12 pi}frac{d}{dt}c^2(t)h(t)$
= $frac{1}{12 pi} left( 2c(t)c'(t)h(t) + c^2(t)h'(t)right)$.
That's as far as one can get until you tell us how $c$ and $h$ vary as functions of $t$.
answered Nov 18 at 3:19
Aditya Dua
5958
answered Nov 18 at 3:19
Aditya Dua
5958
answered Nov 18 at 3:19
Aditya Dua
5958
answered Nov 18 at 3:19
Aditya Dua
5958
5958
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
add a comment |
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
Hi thanks for your answer. So C is the circumference of a tree and H is the height. I need to find the rate of grow or the rate of change of the volume of the tree. As you can see (1/12π)*c^2*h is the formula for the volume of the tree. You're right but at the time of applying the first derivative using the product rule and pulling out the constant 1/12π I left with "c^2+h/6π" as an answer. When checking my result with online calculators the gave me a different answer specifically ch/6π
– David
Nov 18 at 21:08
add a comment |
2
differentiating with respect to what?
– valer
Nov 18 at 0:02
With respect to time (t) so V=volume, (d/d(t)V= d/d(t)(1/12π)*c^2*h
– David
Nov 18 at 0:09
in that case $c$ or $h$ (at least one of them) must be a function of $t$ or else the answer is $0$.
– valer
Nov 18 at 0:13
If you prob write c(t) instead of c, then the online calculators should work (and of course h(t) instead of h)
– Stan Tendijck
Nov 18 at 0:54