Can someone tell me if I am on the right track.... Let z=ln(x^2+y), x=re^t and y=te^r use chain rule and compute ∂z/∂t and ∂z/∂t at point (r,t)=(1,2)

∂z/∂t= ∂f/∂x* ∂x/∂t + ∂f/∂y* ∂y/∂t
∂z/∂r= ∂f/∂x* ∂x/∂r + ∂f/∂y* ∂y/∂r

I find these and then solve for x and y using (r,t)=(1,2) then subsitute the x and y values and the r and t values into ∂z/∂t and ∂z/∂r to get the answer??

Question

Can someone tell me if I am on the right track.... Let z=ln(x^2+y), x=re^t and y=te^r use chain rule and compute ∂z/∂t and ∂z/∂t at point (r,t)=(1,2)

∂z/∂t= ∂f/∂x* ∂x/∂t +  ∂f/∂y* ∂y/∂t
 ∂z/∂r= ∂f/∂x* ∂x/∂r +  ∂f/∂y* ∂y/∂r

I find these and then solve for x and y using (r,t)=(1,2) then subsitute the x and y values and the r and t values into  ∂z/∂t and ∂z/∂r to get the answer??