HI! I do get difficulties on how to perform these partial derivatives qns. EG,If z =f(x,y) is a differentiable f of x and y. where x=rcosA and y=rsinA. my problem is that how to get dz/dr while in the problem there is no more elaborations of z rather than z=f(x,y)?

Question

HI!  I do get difficulties on how to perform these partial derivatives qns. EG,If z =f(x,y) is a differentiable f of x and y. where x=rcosA and y=rsinA. my problem is that how to get dz/dr while in the problem there is no more elaborations of z rather than z=f(x,y)?

anonymous · Answer

F(x,y,z)=f(x,y)-z

anonymous · Answer

well remember chain rule for partial differentiation?
suppose if we have z=f(x,y), and x=f(r,A) and y=f(r,A), so dz/dr is given by
dz/dr=(dz/dy)(dy/dr)+(dz/dx)(dx/dr)=(dz/dy)(sinA)+(dz/dx)(cosA)

anonymous · Answer

if there's no further evaluation of z, I'm afraid this will only be dz/dr

anonymous · Answer

thanks very much anonymoustwo44, your advice worked, I am real enjoying the questions now.