Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 453: 48

$2[cos(2x)e^{sin2x}+cos(e^{2x})(e^{2x})]$

$y'=\frac{d}{dx}[e^{sin2x}+sine^{(2x)}]$ $=\frac{d}{dx}[e^{sin2x}]+\frac{d}{dx}[sine^{(2x)}]$ $=e^{sin2x}\frac{d}{dx}[sin2x]+cos(e^{2x})\frac{d}{dx}[e^{2x}]$ $=e^{sin2x}cos2x.2+cos(e^{2x})(2e^{2x})$ Hence, $=2[cos(2x)e^{sin2x}+cos(e^{2x})(e^{2x})]$