Answer
$-11\sqrt 2$
Work Step by Step
Applying the chain rule, we have
$\frac{d}{dx}[\sin(g(x))]=\cos (g(x))\times g'(x)$
$\frac{d^{2}}{dx^{2}}[\sin(g(x))]_{x=2}=$
$\frac{d}{dx}[\cos (g(x))\times g'(x)]_{x=2}=$
$[-\sin(g(2))g'(2)\times g'(2)]+[\cos(g(2))\times g''(2)]$
(where we applied the chain rule and the product rule)
$=(-\sin \frac{\pi}{4}\times5\times5)+(\cos\frac{\pi}{4}\times3)$
$=-\frac{1}{\sqrt 2}\times25+\frac{1}{\sqrt 2}\times3$
$=-\frac{22}{\sqrt 2}=-11\sqrt 2$
