Derivative of e^(2x)*sin(4x)

Answer

2⋅3253681252⋅x⋅sin(4⋅x)1196962442⋅x+4⋅3253681252⋅x⋅cos(4⋅x)1196962442⋅x\frac{2 \cdot 325368125^{2 \cdot x} \cdot \mathrm{sin}\left(4 \cdot x\right)}{119696244^{2 \cdot x}}+\frac{4 \cdot 325368125^{2 \cdot x} \cdot \mathrm{cos}\left(4 \cdot x\right)}{119696244^{2 \cdot x}}
2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x)

Derivative of e^(2x)*sin(4x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in e2⋅xe^{2 \cdot x}*sin⁡(4⋅x)\sin(4 \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.
  2. Differentiate each factor and combine.
  3. Final answer: 2⋅e2⋅x2 \cdot e^{2 \cdot x}*sin⁡(4⋅x)\sin(4 \cdot x)+4⋅e2⋅x4 \cdot e^{2 \cdot x}*cos⁡(4⋅x)\cos(4 \cdot x)

The derivative of e^(2*x)*sin(4*x) is 2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x).

Instant step-by-step solution for e^(2x)*sin(4x)

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Derivative of e^(2x)*sin(4x) = 2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-2xsin4x

How to find the derivative of e^(2x)*sin(4x)

To find the derivative of e^(2x)*sin(4x), 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^(2x)*sin(4x)?▼
The derivative of e^(2x)*sin(4x) is 2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x).
How do you find the derivative of e^(2x)*sin(4x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x).
Why is the derivative of e^(2x)*sin(4x) equal to 2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(2x)*sin(4x) yields 2*e^(2*x)*sin(4*x)+4*e^(2*x)*cos(4*x). See the full step-by-step breakdown above.

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