If $f$ is a differentiable function, find an expression for the derivative of each of the following functions:

In submitting the answers below, write $f(x)$ as $f$, and write $f'(x)$ as $g$.

(a) If $y=x^2 f(x)$, then $y'=$

(b) If $\displaystyle y=\frac{f(x)}{x^2}$, then $y'=$

(c) If $\displaystyle y=\frac{x^2}{f(x)}$, then $y'=$

(d) If $\displaystyle y=\frac{1+xf(x)}{\sqrt{x}}$, then $y'=$