Calculus • Step-by-Step

Derivative of tan(x) with Steps

Step-by-step differentiation of tan(x). Proved using the quotient rule on sin(x)/cos(x) to yield sec²(x).

Problem Statement

\frac{d}{dx}[\tan(x)]

Final Result

f'(x) = \mathrm{sec}\left(x\right)^{2}

Formula Required: Quotient Rule & Tangent Derivative

Expressing tan(x) as sin(x)/cos(x) and applying quotient rule yields [cos²(x) + sin²(x)]/cos²(x) = 1/cos²(x) = sec²(x).

\frac{d}{dx}[\tan(x)] = \sec^2(x)

2 Steps

Set up the differentiation problem with respect to variable $x$.

\frac{d}{dx} \left[ \mathrm{tan}\left(x\right) \right]

Apply the Tangent Derivative to compute the derivative.

\frac{d}{dx} \left[ \mathrm{tan}\left(x\right) \right] = \mathrm{sec}\left(x\right)^{2}

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

Write tan(x) as sin(x)/cos(x). By quotient rule: (cos·cos - sin·(-sin))/cos² = (cos² + sin²)/cos² = 1/cos² = sec²(x).