Mathematics - Differentiation Question with Solution | TestHub

$u(x)=h(f(g(x)))=h\left(f\left(x^2\right)\right)=h\left(\sin x^2\right)=\log \sin x^2$

Hence, $u^{\prime }(x)=2x\cot x^2$ and $u^{\prime \prime }(x)=2\cot x^2-4x^2{\mathrm{cosec}}^2{x}^2$, so

$u^{\prime \prime }(\sqrt{\pi }/2)=2-2\pi$