Derivada de x^8*atan(x)
Answer
(1+x^2)^(-1)*x^8+8*atan(x)*x^7
Derivative of x^8*atan(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: (1+)^(-1)*+*
A derivada de x^8*atan(x) é (1+x^2)^(-1)*x^8+8*atan(x)*x^7.
Solução passo a passo instantânea para x^8*atan(x)
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Derivative of x^8*atan(x) = (1+x^2)^(-1)*x^8+8*atan(x)*x^7 Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-x-minus-to-minus-the-minus-8atanx
Como encontrar a derivada de x^8*atan(x)
Para encontrar a derivada de x^8*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^8*atan(x)?▼
The derivative of x^8*atan(x) is (1+x^2)^(-1)*x^8+8*atan(x)*x^7.
How do you find the derivative of x^8*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^8+8*atan(x)*x^7.
Why is the derivative of x^8*atan(x) equal to (1+x^2)^(-1)*x^8+8*atan(x)*x^7?▼
Because differentiation measures how a function changes — applying the rules to x^8*atan(x) yields (1+x^2)^(-1)*x^8+8*atan(x)*x^7. See the full step-by-step breakdown above.