# How do you differentiate f(x)=tan(e^(x^2))  using the chain rule?

Jan 31, 2016

here is how,

#### Explanation:

$\frac{d}{\mathrm{dx}} \left(f \left(x\right)\right)$

$= \frac{d}{\mathrm{dx}} \left(\tan \left({e}^{{x}^{2}}\right)\right)$

$= {\sec}^{2} \left({e}^{{x}^{2}}\right) \frac{d}{\mathrm{dx}} \left({e}^{{x}^{2}}\right)$

$= {e}^{{x}^{2}} {\sec}^{2} \left({e}^{{x}^{2}}\right) \frac{d}{\mathrm{dx}} \left({x}^{2}\right)$

$= 2 x {e}^{{x}^{2}} {\sec}^{2} \left({e}^{{x}^{2}}\right)$