# Derivative of tan *x*

How to solve the derivative of tan *x* problems: formula, proof, example, and its solution.

## Formula

The derivative of tan *x* is sec^{2} *x*.

## Proof

Quotient rule in differentiation

1/(cos *x*) = sec *x*

Trigonometric ratio - secant

So 1/(cos^{2} *x*) = sec^{2} *x*.

So [tan *x*]' = sec^{2} *x*.

## Example

*y* = (*x*^{2})(tan *x*)

So *y*' is equal to,

the derivative of *x*^{2}, 2*x*

times tan *x*

plus *x*^{2},

times, the derivative of tan *x*, sec^{2} *x*.

Product rule in differentiation

Power rule in differentiation (Part 1)