Derivative of sin(8x)*cos(8x)

Answer

-8 \cdot \mathrm{sin}\left(8 \cdot x\right)^{2}+8 \cdot \mathrm{cos}\left(8 \cdot x\right)^{2}

Derivative of sin(8x)*cos(8x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $\sin(8 \cdot x)$ * $\cos(8 \cdot x)$ : use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
Differentiate each factor and combine.
Final answer: - $8 \cdot s$ in( $8 \cdot x$ )^2+ $8 \cdot c$ os( $8 \cdot x$ )^2

The derivative of sin(8*x)*cos(8*x) is -8*sin(8*x)^2+8*cos(8*x)^2.

Instant step-by-step solution for sin(8x)*cos(8x)

Derivative TrigonometricIntermediate

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Derivative of sin(8x)*cos(8x) = -8*sin(8*x)^2+8*cos(8*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin8xcos8x

How to find the derivative of sin(8x)*cos(8x)

To find the derivative of sin(8x)*cos(8x), 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(8x)*cos(8x)?▼

The derivative of sin(8x)*cos(8x) is -8*sin(8*x)^2+8*cos(8*x)^2.

How do you find the derivative of sin(8x)*cos(8x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -8*sin(8*x)^2+8*cos(8*x)^2.

Why is the derivative of sin(8x)*cos(8x) equal to -8*sin(8*x)^2+8*cos(8*x)^2?▼

Because differentiation measures how a function changes — applying the rules to sin(8x)*cos(8x) yields -8*sin(8*x)^2+8*cos(8*x)^2. See the full step-by-step breakdown above.

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