# How do you differentiate tan(cos^3(x))?

Use the Chain Rule: $\frac{d}{\mathrm{dx}} \left(\tan \left({\cos}^{3} \left(x\right)\right)\right) = {\sec}^{2} \left({\cos}^{3} \left(x\right)\right) \setminus \cdot \frac{d}{\mathrm{dx}} \left({\cos}^{3} \left(x\right)\right)$
$= {\sec}^{2} \left({\cos}^{3} \left(x\right)\right) \setminus \cdot 3 {\cos}^{2} \left(x\right) \setminus \cdot \left(- \sin \left(x\right)\right)$
$= - 3 \sin \left(x\right) {\cos}^{2} \left(x\right) {\sec}^{2} \left({\cos}^{3} \left(x\right)\right)$