Derivative of e^(5x)*sin(5x)

Answer

\frac{5 \cdot 325368125^{5 \cdot x} \cdot \mathrm{cos}\left(5 \cdot x\right)}{119696244^{5 \cdot x}}+\frac{5 \cdot 325368125^{5 \cdot x} \cdot \mathrm{sin}\left(5 \cdot x\right)}{119696244^{5 \cdot x}}

Derivative of e^(5x)*sin(5x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $e^{5 \cdot x}$ * $\sin(5 \cdot x)$ : 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: $5 \cdot e^{5 \cdot x}$ * $\cos(5 \cdot x)$ + $5 \cdot e^{5 \cdot x}$ * $\sin(5 \cdot x)$

The derivative of e^(5*x)*sin(5*x) is 5*e^(5*x)*cos(5*x)+5*e^(5*x)*sin(5*x).

Instant step-by-step solution for e^(5x)*sin(5x)

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Derivative of e^(5x)*sin(5x) = 5*e^(5*x)*cos(5*x)+5*e^(5*x)*sin(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-5xsin5x

How to find the derivative of e^(5x)*sin(5x)

To find the derivative of e^(5x)*sin(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 e^(5x)*sin(5x)?▼

The derivative of e^(5x)*sin(5x) is 5*e^(5*x)*cos(5*x)+5*e^(5*x)*sin(5*x).

How do you find the derivative of e^(5x)*sin(5x)?▼

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

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

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

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