## Calculus (3rd Edition)

$-11\sqrt 2$
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) $=(-\sin \frac{\pi}{4}\times5\times5)+(\cos\frac{\pi}{4}\times3)$ $=-\frac{1}{\sqrt 2}\times25+\frac{1}{\sqrt 2}\times3$ $=-\frac{22}{\sqrt 2}=-11\sqrt 2$