# Thread: extremely hard partial derivative question

1. ## solved

thanks for the helppp

2. Originally Posted by goaway716
If f_x and f_y are the partial derivatives of f(x,y) and f_s and f_t are the partial derivatives of f viewed as a function of s and t, show that if:

s=(x^3)-(3xy²)

t=3x²y-y^3

then

xf_x+yf_y=3(sf_s+tf_t)

thanx
You need to use the chain rule.

$\displaystyle \displaystyle \frac{\partial f}{\partial x}=\frac{\partial f}{\partial s}\frac{\partial s}{\partial x} + \frac{\partial f}{\partial t}\frac{\partial t}{\partial x}$

$\displaystyle \displaystyle \frac{\partial f}{\partial y}=\frac{\partial f}{\partial s}\frac{\partial s}{\partial y} + \frac{\partial f}{\partial t}\frac{\partial t}{\partial y}$

Then just calculate

$\displaystyle \displaystyle xf_x+yf_y=$ and simplify and sub out x's and y's for s's and t's.

3. ## Re: extremely hard partial derivative question

i have a question and i make a half of it but it is really hard, i had try so many times but did not get the answer.., please help me to find the answer., sorry for my bad english..IMG.pdf.., only number 1 but ignore du/dx+dv/dy=0.., because i already prove it...

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