Calculus • Step-by-Step

Derivative of cos(x) with Steps

Find the derivative of cos(x) step by step. Learn why the derivative of cosine has a negative sign: d/dx[cos(x)] = -sin(x).

Problem Statement

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

Final Result

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

Formula Required: Trigonometric Derivative of Cosine

The slope of the cosine curve at any point equals the negative value of sine at that point.

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

2 Steps

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

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

Apply the Cosine Derivative to compute the derivative.

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

Interactive Calculator

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

Between x = 0 and x = π, the cosine curve is sloping downward (decreasing). Because the slope is negative, the derivative is -sin(x).