Derivative of sin(10*x)+cos(5x)

Answer

-5 \cdot \mathrm{sin}\left(5 \cdot x\right)+10 \cdot \mathrm{cos}\left(10 \cdot x\right)

Derivative of sin(10*x)+cos(5x)

Rule Used: Sum Rule
Steps: Differentiate $\sin(10 \cdot x)$ + $\cos(5 \cdot x)$ term by term. The sum rule says the derivative of a sum is the sum of the derivatives, and the derivative of a constant term is 0, so that term disappears.
Final answer: - $5 \cdot s$ in( $5 \cdot x$ )+ $10 \cdot c$ os( $10 \cdot x$ )

The derivative of sin(10*x)+cos(5*x) is -5*sin(5*x)+10*cos(10*x).

Instant step-by-step solution for sin(10*x)+cos(5x)

Derivative TrigonometricIntermediate

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Derivative of sin(10*x)+cos(5x) = -5*sin(5*x)+10*cos(10*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin10x-minus-plus-minus-cos5x

How to find the derivative of sin(10*x)+cos(5x)

To find the derivative of sin(10*x)+cos(5x), 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(5x)?▼

The derivative of sin(10*x)+cos(5x) is -5*sin(5*x)+10*cos(10*x).

How do you find the derivative of sin(10*x)+cos(5x)?▼

Apply the standard differentiation rules — the key rule used here is the Sum Rule. The step-by-step result is -5*sin(5*x)+10*cos(10*x).

Why is the derivative of sin(10*x)+cos(5x) equal to -5*sin(5*x)+10*cos(10*x)?▼

Because differentiation measures how a function changes — applying the rules to sin(10*x)+cos(5x) yields -5*sin(5*x)+10*cos(10*x). See the full step-by-step breakdown above.

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