Derivative of sin(10x)cos(10*x)

Answer

-10 \cdot \mathrm{sin}\left(10 \cdot x\right)^{2}+10 \cdot \mathrm{cos}\left(10 \cdot x\right)^{2}

Derivative of sin(10x)cos(10*x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $\sin(10 \cdot x)$ * $\cos(10 \cdot x)$ : 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: - $10 \cdot s$ in( $10 \cdot x$ )^2+ $10 \cdot c$ os( $10 \cdot x$ )^2

The derivative of sin(10*x)*cos(10*x) is -10*sin(10*x)^2+10*cos(10*x)^2.

Instant step-by-step solution for sin(10*x)*cos(10*x)

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Derivative of sin(10*x)*cos(10*x) = -10*sin(10*x)^2+10*cos(10*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin10xcos10x

How to find the derivative of sin(10x)cos(10*x)

To find the derivative of sin(10*x)*cos(10*x), 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(10*x)*cos(10*x)?▼

The derivative of sin(10*x)*cos(10*x) is -10*sin(10*x)^2+10*cos(10*x)^2.

How do you find the derivative of sin(10*x)*cos(10*x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -10*sin(10*x)^2+10*cos(10*x)^2.

Why is the derivative of sin(10*x)*cos(10*x) equal to -10*sin(10*x)^2+10*cos(10*x)^2?▼

Because differentiation measures how a function changes — applying the rules to sin(10*x)*cos(10*x) yields -10*sin(10*x)^2+10*cos(10*x)^2. See the full step-by-step breakdown above.

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Derivative of sin(10*x)*cos(10*x)