Calculus • Step-by-Step

Derivative of sin(3x) with Steps

Differentiate sin(3x) using the chain rule. Demonstrates multiplying the outer cosine derivative by the inner 3 to get 3cos(3x).

Problem Statement

\frac{d}{dx}[\sin(3x)]

Final Result

f'(x) = 3 \cdot \mathrm{cos}\left(3 \cdot x\right)

Formula Required: Chain Rule for Trigonometric Functions

The derivative of sin(u) is cos(u) · du/dx.

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

2 Steps

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

\frac{d}{dx} \left[ \mathrm{sin}\left(3 \cdot x\right) \right]

Apply the Chain Rule to compute the derivative.

\frac{d}{dx} \left[ \mathrm{sin}\left(3 \cdot x\right) \right] = 3 \cdot \mathrm{cos}\left(3 \cdot x\right)

Interactive Calculator

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The derivative of sin(3x) is 3cos(3x).