Derivative of x*e^(5x)
Answer
e^(5*x)+5*e^(5*x)*x
Derivative of x*e^(5x)
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in 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: +*x
The derivative of x*e^(5*x) is e^(5*x)+5*e^(5*x)*x.
Instant step-by-step solution for x*e^(5x)
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Derivative of x*e^(5x) = e^(5*x)+5*e^(5*x)*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-xe-minus-to-minus-the-minus-5x
How to find the derivative of x*e^(5x)
To find the derivative of x*e^(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 x*e^(5x)?▼
The derivative of x*e^(5x) is e^(5*x)+5*e^(5*x)*x.
How do you find the derivative of x*e^(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is e^(5*x)+5*e^(5*x)*x.
Why is the derivative of x*e^(5x) equal to e^(5*x)+5*e^(5*x)*x?▼
Because differentiation measures how a function changes — applying the rules to x*e^(5x) yields e^(5*x)+5*e^(5*x)*x. See the full step-by-step breakdown above.