# How do you differentiate  f(x) = tan(sinx)?

Aug 23, 2015

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

#### Explanation:

Use the chain rule:

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

$= {\sec}^{2} \left(\sin x\right) \cdot \left(\cos x\right)$

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