Derivative of x^3*e^x
Answer
e^x*x^3+3*e^x*x^2
Derivative of x^3*e^x
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in *e^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: e^x*+^x*
The derivative of x^3*e^x is e^x*x^3+3*e^x*x^2.
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Derivative of x^3*e^x = e^x*x^3+3*e^x*x^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-3e-minus-to-minus-the-minus-x
How to find the derivative of x^3*e^x
To find the derivative of x^3*e^x, 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^3*e^x?▼
The derivative of x^3*e^x is e^x*x^3+3*e^x*x^2.
How do you find the derivative of x^3*e^x?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is e^x*x^3+3*e^x*x^2.
Why is the derivative of x^3*e^x equal to e^x*x^3+3*e^x*x^2?▼
Because differentiation measures how a function changes — applying the rules to x^3*e^x yields e^x*x^3+3*e^x*x^2. See the full step-by-step breakdown above.