Derivative of x^sin(x)
Answer
(cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x)
Derivative of x^sin(x)
- Rule Used
- Power Rule
- Steps
- Identify the expression as a power function and apply the power rule. A rational exponent is allowed: ^(p/q) = (p/q)·.
- Final answer: (*+*)*x^
The derivative of x^sin(x) is (cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x).
Instant step-by-step solution for x^sin(x)
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Derivative of x^sin(x) = (cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-sinx
How to find the derivative of x^sin(x)
To find the derivative of x^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^sin(x)?▼
The derivative of x^sin(x) is (cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x).
How do you find the derivative of x^sin(x)?▼
Apply the standard differentiation rules — the key rule used here is the Power Rule. The step-by-step result is (cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x).
Why is the derivative of x^sin(x) equal to (cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x)?▼
Because differentiation measures how a function changes — applying the rules to x^sin(x) yields (cos(x)*ln(x)+sin(x)*x^(-1))*x^sin(x). See the full step-by-step breakdown above.