Derivative of x^3*asin(x)

Answer

3 \cdot \mathrm{asin}\left(x\right) \cdot x^{2}+\frac{x^{3}}{\sqrt{-x^{2}+1}}

Derivative of x^3*asin(x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $x^3$ * $\arcsin(x)$ : 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: $3 \cdot a$ $\sin(x)$ * $x^2$ + $\sqrt{-x^2+1}^{-1}$ * $x^3$

The derivative of x^3*asin(x) is 3*asin(x)*x^2+sqrt(-x^2+1)^(-1)*x^3.

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Derivative of x^3*asin(x) = 3*asin(x)*x^2+sqrt(-x^2+1)^(-1)*x^3 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-3asinx

How to find the derivative of x^3*asin(x)

To find the derivative of x^3*asin(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*asin(x)?▼

The derivative of x^3*asin(x) is 3*asin(x)*x^2+sqrt(-x^2+1)^(-1)*x^3.

How do you find the derivative of x^3*asin(x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 3*asin(x)*x^2+sqrt(-x^2+1)^(-1)*x^3.

Why is the derivative of x^3*asin(x) equal to 3*asin(x)*x^2+sqrt(-x^2+1)^(-1)*x^3?▼

Because differentiation measures how a function changes — applying the rules to x^3*asin(x) yields 3*asin(x)*x^2+sqrt(-x^2+1)^(-1)*x^3. See the full step-by-step breakdown above.

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