# What is the Derivative of tan x?

In mathematics, derivatives are very important concepts. Derivatives have various applications in almost every discipline of engineering and science. Derivative also used to find the function's maximum or minimum values and it is also used to predict the monotonicity of a given function.

## Answer: The derivative of tan x is sec^{2}x.

Let's understand how we arrived at the solution.

**Explanation:**

Let,

y = tan x

y = sin x / cos x [ since, tanx = sin x / cos x]

Differentiating w.r.t x

dy/dx = [d/dx(sin x) × cos x – d/dx( cos x) × sin x] / [cos^{2}x] (using quotient rule)

dy/dx = [cos x × cos x + sin x × sin x] / [cos^{2}x]

dy/dx = [cos^{2} x + sin^{2}x] / [cos^{2}x]

dy/dx = [1 / (cos^{2}x)] [ since, cos^{2} x + sin^{2}x =1 ]

Now, subsitute [1 / (cos^{2}x)] = sec^{2}x

dy/dx = sec^{2}x

Also, we can check out the online derivative calculator to verify our answer.

### Hence, the derivative of tan x is sec^{2}x.

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