Finding the second order partial derivative of an arbitrary function.
I need to find the higher order partial derivative of a function. (Need to find: $frac{delta ^2 f}{delta u^2}$ and $frac{delta ^2 f}{delta v^2}$)
The problem is that the function is not specified only given as a function of x and y.
$f(x,y)$
It's also been given that $x=Au + Bv$ and that $y=Cu + Dv$ (Kindly note that the uppercase letters are constants not variables)
I have managed to get till the first partial derivatives. I.e. $frac{(delta f)}{(delta u)}$ and $frac{(delta f)}{(delta v)}$
Unfortunately getting to the second derivative is where I'm completely stumped, all the solutions I found online aren't applicable as they require that the function isn't arbitrary.
Any help would be super appreciated
partial-derivative
asked Nov 28 '18 at 20:53
MadMathWiz
435
add a comment |
I need to find the higher order partial derivative of a function. (Need to find: $frac{delta ^2 f}{delta u^2}$ and $frac{delta ^2 f}{delta v^2}$)
The problem is that the function is not specified only given as a function of x and y.
$f(x,y)$
It's also been given that $x=Au + Bv$ and that $y=Cu + Dv$ (Kindly note that the uppercase letters are constants not variables)
I have managed to get till the first partial derivatives. I.e. $frac{(delta f)}{(delta u)}$ and $frac{(delta f)}{(delta v)}$
Unfortunately getting to the second derivative is where I'm completely stumped, all the solutions I found online aren't applicable as they require that the function isn't arbitrary.
Any help would be super appreciated
partial-derivative
asked Nov 28 '18 at 20:53
MadMathWiz
435
If I understand the question correctly, what you want is $partial^2 f/partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$?
– Hans Lundmark
Nov 28 '18 at 21:00
Hi, yes that's correct
– MadMathWiz
Nov 28 '18 at 21:12
add a comment |
I need to find the higher order partial derivative of a function. (Need to find: $frac{delta ^2 f}{delta u^2}$ and $frac{delta ^2 f}{delta v^2}$)
The problem is that the function is not specified only given as a function of x and y.
$f(x,y)$
It's also been given that $x=Au + Bv$ and that $y=Cu + Dv$ (Kindly note that the uppercase letters are constants not variables)
I have managed to get till the first partial derivatives. I.e. $frac{(delta f)}{(delta u)}$ and $frac{(delta f)}{(delta v)}$
Unfortunately getting to the second derivative is where I'm completely stumped, all the solutions I found online aren't applicable as they require that the function isn't arbitrary.
Any help would be super appreciated
partial-derivative
asked Nov 28 '18 at 20:53
MadMathWiz
435
I need to find the higher order partial derivative of a function. (Need to find: $frac{delta ^2 f}{delta u^2}$ and $frac{delta ^2 f}{delta v^2}$)
The problem is that the function is not specified only given as a function of x and y.
$f(x,y)$
It's also been given that $x=Au + Bv$ and that $y=Cu + Dv$ (Kindly note that the uppercase letters are constants not variables)
I have managed to get till the first partial derivatives. I.e. $frac{(delta f)}{(delta u)}$ and $frac{(delta f)}{(delta v)}$
Unfortunately getting to the second derivative is where I'm completely stumped, all the solutions I found online aren't applicable as they require that the function isn't arbitrary.
Any help would be super appreciated
partial-derivative
partial-derivative
asked Nov 28 '18 at 20:53
MadMathWiz
435
asked Nov 28 '18 at 20:53
MadMathWiz
435
edited Nov 28 '18 at 21:15
asked Nov 28 '18 at 20:53
MadMathWiz
435
asked Nov 28 '18 at 20:53
MadMathWiz
435
asked Nov 28 '18 at 20:53
MadMathWiz
435
435
If I understand the question correctly, what you want is $partial^2 f/partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$?
– Hans Lundmark
Nov 28 '18 at 21:00
Hi, yes that's correct
– MadMathWiz
Nov 28 '18 at 21:12
add a comment |
If I understand the question correctly, what you want is $partial^2 f/partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$?
– Hans Lundmark
Nov 28 '18 at 21:00
Hi, yes that's correct
– MadMathWiz
Nov 28 '18 at 21:12
If I understand the question correctly, what you want is $partial^2 f/partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$?
– Hans Lundmark
Nov 28 '18 at 21:00
If I understand the question correctly, what you want is $partial^2 f/partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$?
– Hans Lundmark
Nov 28 '18 at 21:00
Hi, yes that's correct
– MadMathWiz
Nov 28 '18 at 21:12
Hi, yes that's correct
– MadMathWiz
Nov 28 '18 at 21:12
add a comment |
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If I understand the question correctly, what you want is $partial^2 f/partial u^2$ (etc.) in terms of derivatives with respect to the old variables $x$ and $y$?
– Hans Lundmark
Nov 28 '18 at 21:00
Hi, yes that's correct
– MadMathWiz
Nov 28 '18 at 21:12