Single-fraction derivatives and an implicit slope

(a) Differentiate the following with respect to $x$, giving your answers as single fractions.

(i) $\ln\left(\dfrac{x}{\sqrt{1-2x}}\right)$,

(ii) $\dfrac1{\cos^{-1}(x^2)}$.

(b) The variables $x$ and $y$ are related by $e^{xy^2}=y(x^2+2e^x)$.

Find the value of $\dfrac{dy}{dx}$ when $x=0$ and $y=\dfrac12$.