1. The problem statement, all variables and given/known data Write the chain rule for the following composition using a tree diagram: z =g(x,y) where x=x(r,theta) and y=y(r,theta). Write formulas for the partial derivatives dz/dr and dz/dtheta. Use them to answer: Find first partial derivatives of the function z=e^x+yx^2, in polar coordinates, that is find dz/dr and dz/dtheta as a function of polar coordinates (r, theta). 2. Relevant equations 3. The attempt at a solution Tree diagram was relatively simple g extends to x and y. x and y both extend to r and theta. **all "d's" symbolize partial derivatives** dz/dr = dg/dx*dx/dr+ dg/dy*dy/dr dz/dtheta = dg/dx*dx/dtheta+dg/dy*dy/dtheta Ok. So partial x = e^x+2yx partial y = x^2 Now the problem I'm having trouble with is taking the partial derivative of the polar coordinate functions. If I am right, then: x=rcos(theta) y=rsin(theta) Taking the partial derivatives dx/dr and dy/dr the answers would be cos(theta) for x and sin(theta) for y, as we treat these as 'constants'. From here it is merely a plug-n-chug. Is this correct? Do you have any opinions? Thank you.