Question

If f(x) = e^(tan^2)x, then f'(x)=

Answer 1

$\large f(x)=e^{\tan^2x} \\ \\ \large f'(x)=(e^{\tan^2x})'=e^{\tan^2x}(\tan^2{x})'=e^{\tan^2x}\times2\tan{x}(\tan{x})'= \\ \\=2e^{\tan^2x}\tan{x}( \frac{\sin{x}}{\cos{x}} )'=2e^{\tan^2x}\tan{x} \frac{1}{\cos^2{x}} =2e^{\tan^2x} \times\frac{\sin{x}}{\cos{x}} \frac{1}{\cos^2{x}} = \\ \\=2e^{\tan^2x} \times\frac{\sin{x}}{\cos^3{x}} }$