Question

What is the derivative of $\tan \left(2x\right)$?

Answer 1

Find the derivative of $\tan \left(2x\right)$.

Let, $y=\tan \left(2x\right)$

Differentiate both sides w.r.t $x$ using chain rule.

$$\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}\tan \left(2x\right) \\ ={\sec }^{2}2x\times \frac{d}{dx}\left(2x\right)\left[\because \frac{d}{dx}\tan \left(2x\right)={\sec }^{2}2x\right] \\ ={\sec }^{2}2x\times 2 \\ =2{\sec }^{2}2x \end{gathered}$$

Therefore, the derivative of $\tan \left(2x\right)$ is $2{\sec }^{2}2x$.