Chapter 2 - Derivatives - Review - Exercises - Page 198: 71

$$h^{\prime}(x) =4f^{\prime}(g(\sin 4 x)) g^{\prime}(\sin 4 x)(\cos 4 x) $$

Given $$h(x)=f(g(\sin 4x)) $$ Then \begin{align*} h^{\prime}(x)&=f^{\prime}(g(\sin 4 x)) \cdot \frac{d}{d x}(g(\sin 4 x))\\ &=f^{\prime}(g(\sin 4 x)) \cdot g^{\prime}(\sin 4 x) \cdot \frac{d}{d x}(\sin 4 x)\\ &=f^{\prime}(g(\sin 4 x)) g^{\prime}(\sin 4 x)(\cos 4 x)(4) \end{align*}