Originally Posted by

**Chris L T521** By definition:

$\displaystyle \frac{\partial f}{\partial\theta}=\frac{\partial f}{\partial x}\cdot\frac{\,dx}{\,d\theta}+\frac{\partial f}{\partial y}\cdot\frac{\,dy}{\,d\theta}$

Since $\displaystyle f\left(x,y\right)=x^2+y^2$, when we partially differentiate the function wrt one variable, we hold the other variable constant. As a result, $\displaystyle \frac{\partial f}{\partial x}=2x$. I leave it for you to find $\displaystyle \frac{\partial f}{\partial y}$. You also need to find $\displaystyle \frac{\,dx}{\,d\theta}$ and $\displaystyle \frac{\,dy}{\,d\theta}$. You can easily do these since x and y are defined in terms of theta, and also because this is ordinary differentiation.

When you plug all those values into the equation, try to get your result in terms of one variable, $\displaystyle \theta$.

Can you take it from here?