Calculus • Step-by-Step

Derivative of sin(x) with Steps

Learn how to differentiate sin(x) step by step. Proves why d/dx[sin(x)] = cos(x) with clear explanations and formulas.

Problem Statement

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

Final Result

f'(x) = \mathrm{cos}\left(x\right)

Formula Required: Trigonometric Derivative of Sine

The instantaneous rate of change of the sine function is the cosine function.

\frac{d}{dx}[\sin(x)] = \cos(x)

2 Steps

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

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

Apply the Sine Derivative to compute the derivative.

\frac{d}{dx} \left[ \mathrm{sin}\left(x\right) \right] = \mathrm{cos}\left(x\right)

Interactive Calculator

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

From the limit definition of the derivative and angle sum identities, lim(h→0) [sin(x+h) - sin(x)]/h simplifies directly to cos(x).