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Topic: Derivative of a multivariable function by another multivariable function
Replies: 10   Last Post: Apr 10, 2013 9:08 AM

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William Elliot

Posts: 1,533
Registered: 1/8/12
Re: Derivative of a multivariable function by another multivariable
function

Posted: Apr 6, 2013 3:12 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Fri, 5 Apr 2013, henuaenata wrote:
>
> I am trying to figure out how to write the derivative of a multivariable
> function by another multivariable function.
>
> For example, how to derive f(x,y,z) with respect to g(x,y):

âHBf(x,y,z)/âHBg(x,y)

First off, don't use fancy confusing characters, use plain text only.
Secondaly, I doubt there is such a thing. However, symbolically

df(x,y,z)/dt = f_x(x,y,z).dx/dt + f_y(x,y,z).dy/dt + f_z(x,y,z).dz/dt

Let t = g(x,y); dz/dt = 0; dt/dx = g_x(x,y); dt/dy = g_y(x,y),
df(x,y,z)/dg(x,y) = f_x(x,y,z)/g_x(x,y) + f_y(x,y,z)/g_y(x,y).



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