Derivative of sin(9x)*cos(9x)

Answer

-9 \cdot \mathrm{sin}\left(9 \cdot x\right)^{2}+9 \cdot \mathrm{cos}\left(9 \cdot x\right)^{2}

Derivative of sin(9x)*cos(9x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $\sin(9 \cdot x)$ * $\cos(9 \cdot x)$ : 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: - $9 \cdot s$ in( $9 \cdot x$ )^2+ $9 \cdot c$ os( $9 \cdot x$ )^2

The derivative of sin(9*x)*cos(9*x) is -9*sin(9*x)^2+9*cos(9*x)^2.

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Derivative TrigonometricIntermediate

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Derivative of sin(9x)*cos(9x) = -9*sin(9*x)^2+9*cos(9*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin9xcos9x

How to find the derivative of sin(9x)*cos(9x)

To find the derivative of sin(9x)*cos(9x), 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(9x)*cos(9x)?▼

The derivative of sin(9x)*cos(9x) is -9*sin(9*x)^2+9*cos(9*x)^2.

How do you find the derivative of sin(9x)*cos(9x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -9*sin(9*x)^2+9*cos(9*x)^2.

Why is the derivative of sin(9x)*cos(9x) equal to -9*sin(9*x)^2+9*cos(9*x)^2?▼

Because differentiation measures how a function changes — applying the rules to sin(9x)*cos(9x) yields -9*sin(9*x)^2+9*cos(9*x)^2. See the full step-by-step breakdown above.

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