Derivative of x^10*atan(x)

Answer

\frac{x^{10}}{x^{2}+1}+10 \cdot \mathrm{atan}\left(x\right) \cdot x^{9}

Derivative of x^10*atan(x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $x^10$ * $\arctan(x)$ : 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)* $x^10$ + $10 \cdot a$ $\tan(x)$ * $x^9$

The derivative of x^10*atan(x) is (1+x^2)^(-1)*x^10+10*atan(x)*x^9.

Instant step-by-step solution for x^10*atan(x)

Derivative PolynomialBeginner

Share this result

Share on X

Derivative of x^10*atan(x) = (1+x^2)^(-1)*x^10+10*atan(x)*x^9 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-10atanx

How to find the derivative of x^10*atan(x)

To find the derivative of x^10*atan(x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

Practice More Problems

Derivative of acos(x)

Solve d/dx acos(x)

Derivative of asin(x)

Solve d/dx asin(x)

Derivative of atan(x)

Solve d/dx atan(x)

Derivative of x^(1/3)

Solve d/dx x^(1/3)

Derivative of cos(2x)

Solve d/dx cos(2x)

Derivative of cos(x)^2

Solve d/dx cos(x)^2

Derivative of cos(x)

Solve d/dx cos(x)

Frequently Asked Questions

What is the derivative of x^10*atan(x)?▼

The derivative of x^10*atan(x) is (1+x^2)^(-1)*x^10+10*atan(x)*x^9.

How do you find the derivative of x^10*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^10+10*atan(x)*x^9.

Why is the derivative of x^10*atan(x) equal to (1+x^2)^(-1)*x^10+10*atan(x)*x^9?▼

Because differentiation measures how a function changes — applying the rules to x^10*atan(x) yields (1+x^2)^(-1)*x^10+10*atan(x)*x^9. See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️