# Derivative of tan square x | tan^2x derivative

The derivative of tan square x is equal to 2tanx sec2x. Here we find the derivative of tan2x by the chain and product rule. The derivative formula of tan square x is given below:

$\dfrac{d}{dx}(\tan^2 x)=2 \tan x \sec^2x$.

## What is the derivative of tan square x?

Let us find the derivative of tan2x by the chain rule. To do so, let us put

z=tanx.

So $\dfrac{dz}{dx}=\sec^2 x$.

Now, by the chain rule, the derivative of tan square x will be equal to

$\dfrac{d}{dx}(\tan^2 x)$ = $\dfrac{d}{dx}(z^2) \times \dfrac{dz}{dx}$

= 2z × sec2x by the power rule of integration: d/dx(xn) = nxn-1.

= 2tanx sec2x as z=tanx.

So the derivative of tan square x is equal to 2tanx sec2x, and this is proved by the chain rule of derivatives.

## Derivative of tan2x by Product Rule

Note that tan2x is a product of two times of tanx. So the derivative of tan2x by the product rule is equal to

$\dfrac{d}{dx}(\tan^2 x)$ = $\dfrac{d}{dx}(\tan x \cdot \tan x)$

= tan x $\dfrac{d}{dx}(\tan x)$ + tan x $\dfrac{d}{dx}(\tan x)$

= tanx sec2x + tanx sec2x as the derivative of tanx is sec2x.

= 2tanx sec2x.

So the derivative of tan2x is tanx sec2x, and this is obtained by the product rule of derivatives.

## FAQs

Q1: If y=tan2x, then find dy/dx?

Answer: The derivative of y=tan2x is dy/dx = 2 tanx sec2x.

Q2: What is the derivative of tan2x?

Answer: The derivative of tan2x is 2sec2x tanx.