Calculus • Step-by-Step

Derivative of cos(2x) with Steps

Differentiate cos(2x) step by step using the Chain Rule. Identifies the inner function u = 2x and outer function cos(u) to yield -2sin(2x).

Problem Statement

\frac{d}{dx}[\cos(2x)]

Final Result

f'(x) = -2 \cdot \mathrm{sin}\left(2 \cdot x\right)

Formula Required: Chain Rule for Trigonometry

Differentiate cosine to -sine and multiply by the internal coefficient k.

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

2 Steps

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

\frac{d}{dx} \left[ \mathrm{cos}\left(2 \cdot x\right) \right]

Apply the Chain Rule to compute the derivative.

\frac{d}{dx} \left[ \mathrm{cos}\left(2 \cdot x\right) \right] = -2 \cdot \mathrm{sin}\left(2 \cdot x\right)

Interactive Calculator

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

The derivative of cos(2x) is -2sin(2x), found by chain rule: -sin(2x) · 2.