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