Derivative of e^(6x)*sin(3x)

Answer

\frac{3 \cdot 325368125^{6 \cdot x} \cdot \mathrm{cos}\left(3 \cdot x\right)}{119696244^{6 \cdot x}}+\frac{6 \cdot 325368125^{6 \cdot x} \cdot \mathrm{sin}\left(3 \cdot x\right)}{119696244^{6 \cdot x}}

Derivative of e^(6x)*sin(3x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $e^{6 \cdot x}$ * $\sin(3 \cdot x)$ : 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: $3 \cdot e^{6 \cdot x}$ * $\cos(3 \cdot x)$ + $6 \cdot e^{6 \cdot x}$ * $\sin(3 \cdot x)$

The derivative of e^(6*x)*sin(3*x) is 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x).

Instant step-by-step solution for e^(6x)*sin(3x)

Derivative ExponentialIntermediate

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Derivative of e^(6x)*sin(3x) = 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-6xsin3x

How to find the derivative of e^(6x)*sin(3x)

To find the derivative of e^(6x)*sin(3x), 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^(6x)*sin(3x)?▼

The derivative of e^(6x)*sin(3x) is 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x).

How do you find the derivative of e^(6x)*sin(3x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x).

Why is the derivative of e^(6x)*sin(3x) equal to 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x)?▼

Because differentiation measures how a function changes — applying the rules to e^(6x)*sin(3x) yields 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x). See the full step-by-step breakdown above.

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