Partial derivatives/ total derivative

by zell99
Tags: derivative, derivatives or, partial
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,510 You have the definitions. All I can say is "just do it"! You are asked to show that $$\frac{\partial f}{\partial x}= u\frac{\partial F}{\partial u}+ v\frac{\partial F}{\partial v}$$ u= excos(y), v= exsin(y) and F(u,v)= f(x,y). You will need to use the chain rule: $$\frac{\partial f}{\partial x}= \frac{\partial F}{\partial u}\frac{\partial u}{\partial x}+ \frac{\partial F}{\partial v}\frac{\partial v}{\partial x}$$