Derivative of x^5*sin(x)
Answer
5*sin(x)*x^4+cos(x)*x^5
Derivative of x^5*sin(x)
- 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: in(x)*+*
The derivative of x^5*sin(x) is 5*sin(x)*x^4+cos(x)*x^5.
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Derivative of x^5*sin(x) = 5*sin(x)*x^4+cos(x)*x^5 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-5sinx
How to find the derivative of x^5*sin(x)
To find the derivative of x^5*sin(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^5*sin(x)?▼
The derivative of x^5*sin(x) is 5*sin(x)*x^4+cos(x)*x^5.
How do you find the derivative of x^5*sin(x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 5*sin(x)*x^4+cos(x)*x^5.
Why is the derivative of x^5*sin(x) equal to 5*sin(x)*x^4+cos(x)*x^5?▼
Because differentiation measures how a function changes — applying the rules to x^5*sin(x) yields 5*sin(x)*x^4+cos(x)*x^5. See the full step-by-step breakdown above.