Chain rule of partial derivatives for composite functions.

Function of the form

$$f({x}^{2}+{y}^{2})$$

How do I find the partial derivatives

$$\frac{\mathrm{\partial}f}{\mathrm{\partial}y},\frac{\mathrm{\partial}f}{\mathrm{\partial}x}$$

How $f({x}^{2}+{y}^{2})$ behaves. Assuming it should of the form

$$g(x,y)\cdot 2y\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}h(x,y)\cdot 2x$$

Function of the form

$$f({x}^{2}+{y}^{2})$$

How do I find the partial derivatives

$$\frac{\mathrm{\partial}f}{\mathrm{\partial}y},\frac{\mathrm{\partial}f}{\mathrm{\partial}x}$$

How $f({x}^{2}+{y}^{2})$ behaves. Assuming it should of the form

$$g(x,y)\cdot 2y\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}h(x,y)\cdot 2x$$