Derivative of e^(4x)*sin(2x)
Answer
2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x)
Derivative of e^(4x)*sin(2x)
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in *: 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: *+*
The derivative of e^(4*x)*sin(2*x) is 2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x).
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Derivative of e^(4x)*sin(2x) = 2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-4xsin2x
How to find the derivative of e^(4x)*sin(2x)
To find the derivative of e^(4x)*sin(2x), 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^(4x)*sin(2x)?▼
The derivative of e^(4x)*sin(2x) is 2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x).
How do you find the derivative of e^(4x)*sin(2x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x).
Why is the derivative of e^(4x)*sin(2x) equal to 2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(4x)*sin(2x) yields 2*e^(4*x)*cos(2*x)+4*e^(4*x)*sin(2*x). See the full step-by-step breakdown above.