Question

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

Answer 1

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

Differentiate both sides, w.r.t$x$.

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

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