Derivada de x^9*atan(x)

Answer

\frac{x^{9}}{x^{2}+1}+9 \cdot \mathrm{atan}\left(x\right) \cdot x^{8}

Derivative of x^9*atan(x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $x^9$ * $\arctan(x)$ : 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)* $x^9$ + $9 \cdot a$ $\tan(x)$ * $x^8$

A derivada de x^9*atan(x) é (1+x^2)^(-1)*x^9+9*atan(x)*x^8.

Solução passo a passo instantânea para x^9*atan(x)

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Derivative of x^9*atan(x) = (1+x^2)^(-1)*x^9+9*atan(x)*x^8 Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-x-minus-to-minus-the-minus-9atanx

Como encontrar a derivada de x^9*atan(x)

Para encontrar a derivada de x^9*atan(x), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a lógica.

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Frequently Asked Questions

What is the derivative of x^9*atan(x)?▼

The derivative of x^9*atan(x) is (1+x^2)^(-1)*x^9+9*atan(x)*x^8.

How do you find the derivative of x^9*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^9+9*atan(x)*x^8.

Why is the derivative of x^9*atan(x) equal to (1+x^2)^(-1)*x^9+9*atan(x)*x^8?▼

Because differentiation measures how a function changes — applying the rules to x^9*atan(x) yields (1+x^2)^(-1)*x^9+9*atan(x)*x^8. See the full step-by-step breakdown above.

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