Solutions

a)

$$g'=2f\cdot f'$$

b)

$$g'=((f')^2)'=2f'\cdot f''$$

c) Differentiating both sides of the equation, we get

$$2f'f''=f'-\frac{3}{f^4}f'\implies f''=\frac{1}{2}-\frac{3}{2f^4},$$

assuming that $f'\ne0$.