Problem

The curve $C$ has equation

$$xy^3-4x^3y=3.$$

(a) Show that, at the point $(-1,1)$ on $C$, $\dfrac{\mathrm{d}y}{\mathrm{d}x}=11$.

(b) Find the value of $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}$ at the point $(-1,1)$.