Derivative of x^3*atan(x)

Answer

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

Derivative of x^3*atan(x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $x^3$ * $\arctan(x)$ : 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: (1+ $x^2$ )^(-1)* $x^3$ + $3 \cdot a$ $\tan(x)$ * $x^2$

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

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

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

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

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

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

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

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

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

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