Derivative of sin(4x)

Answer

4 \cdot \mathrm{cos}\left(4 \cdot x\right)

Derivative of sin(4x)

Rule Used: Chain Rule
Steps: Identify a composite function in $\sin(4 \cdot x)$ : use the chain rule $\frac{d}{dx} f(g(x))$ = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
Differentiate the outer function, then multiply by the inner derivative.
Final answer: $4 \cdot c$ os( $4 \cdot x$ )

The derivative of sin(4*x) is 4*cos(4*x).

Instant step-by-step solution for sin(4x)

Derivative TrigonometricIntermediate

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Derivative of sin(4x) = 4*cos(4*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin4x

How to find the derivative of sin(4x)

To find the derivative of sin(4x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

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Frequently Asked Questions

What is the derivative of sin(4x)?▼

The derivative of sin(4x) is 4*cos(4*x).

How do you find the derivative of sin(4x)?▼

Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 4*cos(4*x).

Why is the derivative of sin(4x) equal to 4*cos(4*x)?▼

Because differentiation measures how a function changes — applying the rules to sin(4x) yields 4*cos(4*x). See the full step-by-step breakdown above.

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