Derivative of tan x

Derivative of tan x

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

Formula

[tan x]' = sec^2 x

The derivative of tan x is sec2 x.

Proof

Derivative of tan x: Proof of the Formula

Quotient identities

Quotient rule in differentiation

Pythagorean identities

1/(cos x) = sec x

Trigonometric ratio - secant

So 1/(cos2 x) = sec2 x.

So [tan x]' = sec2 x.

Example

Find the derivative of the given function. y = x^2 tan x

y = (x2)(tan x)

So y' is equal to,
the derivative of x2, 2x
times tan x
plus x2,
times, the derivative of tan x, sec2 x.

Product rule in differentiation

Power rule in differentiation (Part 1)