How to find these derivatives of a implicit function.
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The equation
$x^3 + 2y^3 + z^3 + xyz = 4$
$x,y > 0$ describe a graph of a function: $ z = f(x,y)$.
Find, $frac{partial f}{partial x}$ and $ frac{partial^2 f}{partial xpartial y}$
So I know how to find the first one, you just take the derivative in accordance to x, but I'm confused on how to do the second one.
calculus multivariable-calculus partial-derivative
asked Dec 5 at 2:53
mathkid225
1227
add a comment |
up vote
1
down vote
favorite
The equation
$x^3 + 2y^3 + z^3 + xyz = 4$
$x,y > 0$ describe a graph of a function: $ z = f(x,y)$.
Find, $frac{partial f}{partial x}$ and $ frac{partial^2 f}{partial xpartial y}$
So I know how to find the first one, you just take the derivative in accordance to x, but I'm confused on how to do the second one.
calculus multivariable-calculus partial-derivative
asked Dec 5 at 2:53
mathkid225
1227
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The equation
$x^3 + 2y^3 + z^3 + xyz = 4$
$x,y > 0$ describe a graph of a function: $ z = f(x,y)$.
Find, $frac{partial f}{partial x}$ and $ frac{partial^2 f}{partial xpartial y}$
So I know how to find the first one, you just take the derivative in accordance to x, but I'm confused on how to do the second one.
calculus multivariable-calculus partial-derivative
asked Dec 5 at 2:53
mathkid225
1227
The equation
$x^3 + 2y^3 + z^3 + xyz = 4$
$x,y > 0$ describe a graph of a function: $ z = f(x,y)$.
Find, $frac{partial f}{partial x}$ and $ frac{partial^2 f}{partial xpartial y}$
So I know how to find the first one, you just take the derivative in accordance to x, but I'm confused on how to do the second one.
calculus multivariable-calculus partial-derivative
calculus multivariable-calculus partial-derivative
asked Dec 5 at 2:53
mathkid225
1227
asked Dec 5 at 2:53
mathkid225
1227
asked Dec 5 at 2:53
mathkid225
1227
asked Dec 5 at 2:53
mathkid225
1227
asked Dec 5 at 2:53
mathkid225
1227
1227
add a comment |
add a comment |
1 Answer
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up vote
1
down vote
accepted
The second one is probably better notated as follows:
$$frac{partial f^2}{partial x partial y} = frac{partial}{partial x} left( frac{partial f}{partial y} right)$$
In other words, you just find the partial derivative of $f$ with respect to $y$, and then find the partial derivative of that with respect to $x$. The notation is a little unintuitive so I can see the confusion.
answered Dec 5 at 2:59
Eevee Trainer
3,320225
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
The second one is probably better notated as follows:
$$frac{partial f^2}{partial x partial y} = frac{partial}{partial x} left( frac{partial f}{partial y} right)$$
In other words, you just find the partial derivative of $f$ with respect to $y$, and then find the partial derivative of that with respect to $x$. The notation is a little unintuitive so I can see the confusion.
answered Dec 5 at 2:59
Eevee Trainer
3,320225
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
add a comment |
up vote
1
down vote
accepted
The second one is probably better notated as follows:
$$frac{partial f^2}{partial x partial y} = frac{partial}{partial x} left( frac{partial f}{partial y} right)$$
In other words, you just find the partial derivative of $f$ with respect to $y$, and then find the partial derivative of that with respect to $x$. The notation is a little unintuitive so I can see the confusion.
answered Dec 5 at 2:59
Eevee Trainer
3,320225
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
The second one is probably better notated as follows:
$$frac{partial f^2}{partial x partial y} = frac{partial}{partial x} left( frac{partial f}{partial y} right)$$
In other words, you just find the partial derivative of $f$ with respect to $y$, and then find the partial derivative of that with respect to $x$. The notation is a little unintuitive so I can see the confusion.
answered Dec 5 at 2:59
Eevee Trainer
3,320225
The second one is probably better notated as follows:
$$frac{partial f^2}{partial x partial y} = frac{partial}{partial x} left( frac{partial f}{partial y} right)$$
In other words, you just find the partial derivative of $f$ with respect to $y$, and then find the partial derivative of that with respect to $x$. The notation is a little unintuitive so I can see the confusion.
answered Dec 5 at 2:59
Eevee Trainer
3,320225
answered Dec 5 at 2:59
Eevee Trainer
3,320225
answered Dec 5 at 2:59
Eevee Trainer
3,320225
answered Dec 5 at 2:59
Eevee Trainer
3,320225
3,320225
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
add a comment |
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
okay I see, so would I take the partial in respect to dx after finding the derivative with respect to dy?
– mathkid225
Dec 5 at 3:06
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
Yup, that's right!
– Eevee Trainer
Dec 5 at 3:07
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
ugh, I'm still stuck, how would you write this out in terms of the chain rule?
– mathkid225
Dec 5 at 3:36
add a comment |
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