Originally Posted by

**mechaniac** $\displaystyle f(x,y)$

For all s,t :

$\displaystyle f(s,8s)=6s+cos(6s)$

$\displaystyle f(t,-7t)=1+6t+5t^2$

Determin $\displaystyle \frac{\partial f}{\partial x}(0,0) $ and $\displaystyle \frac{\partial f}{\partial y}(0,0) $

Im new to multi variables so i donīt know how to do this.

I thought if i set $\displaystyle z=f(x(s,t),y(s,t))$

i get:

$\displaystyle \frac{\partial z}{\partial s }= \frac{\partial z}{\partial x}\frac{\partial x}{\partial s}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial s} $

$\displaystyle \frac{\partial z}{\partial t }= \frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial z}{\partial y}\frac{\partial y}{\partial t} $

from here i donīt know what to do.

Thanks!