Derivative of sin(2x)+cos(5x)

Answer

-5 \cdot \mathrm{sin}\left(5 \cdot x\right)+2 \cdot \mathrm{cos}\left(2 \cdot x\right)

Derivative of sin(2x)+cos(5x)

Rule Used: Sum Rule
Steps: Differentiate $\sin(2 \cdot x)$ + $\cos(5 \cdot x)$ 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( $5 \cdot x$ )+ $2 \cdot c$ os( $2 \cdot x$ )

The derivative of sin(2*x)+cos(5*x) is -5*sin(5*x)+2*cos(2*x).

Instant step-by-step solution for sin(2x)+cos(5x)

Derivative TrigonometricIntermediate

Share this result

Share on X

Derivative of sin(2x)+cos(5x) = -5*sin(5*x)+2*cos(2*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-sin2x-minus-plus-minus-cos5x

How to find the derivative of sin(2x)+cos(5x)

To find the derivative of sin(2x)+cos(5x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

Practice More Problems

Derivative of acos(x)

Solve d/dx acos(x)

Derivative of asin(x)

Solve d/dx asin(x)

Derivative of atan(x)

Solve d/dx atan(x)

Derivative of x^(1/3)

Solve d/dx x^(1/3)

Frequently Asked Questions

What is the derivative of sin(2x)+cos(5x)?▼

The derivative of sin(2x)+cos(5x) is -5*sin(5*x)+2*cos(2*x).

How do you find the derivative of sin(2x)+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)+2*cos(2*x).

Why is the derivative of sin(2x)+cos(5x) equal to -5*sin(5*x)+2*cos(2*x)?▼

Because differentiation measures how a function changes — applying the rules to sin(2x)+cos(5x) yields -5*sin(5*x)+2*cos(2*x). See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️