Derivada de x^4*atan(x)
Answer
(1+x^2)^(-1)*x^4+4*atan(x)*x^3
Derivative of x^4*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^4*atan(x) é (1+x^2)^(-1)*x^4+4*atan(x)*x^3.
Solução passo a passo instantânea para x^4*atan(x)
Share this result
Derivative of x^4*atan(x) = (1+x^2)^(-1)*x^4+4*atan(x)*x^3 Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-x-minus-to-minus-the-minus-4atanx
Como encontrar a derivada de x^4*atan(x)
Para encontrar a derivada de x^4*atan(x), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a lógica.
Praticar Mais Problemas
Derivada de x^3
Resolver d/dx x^3
Derivada de x*e^x
Resolver d/dx x*e^x
Derivada de x*ln(x)
Resolver d/dx x*ln(x)
Derivada de x+1
Resolver d/dx x+1
Derivada de x*sin(x)
Resolver d/dx x*sin(x)
Derivada de x^2
Resolver d/dx x^2
Derivada de x^2-1
Resolver d/dx x^2-1
Derivada de x^2+1
Resolver d/dx x^2+1
Derivada de x^4
Resolver d/dx x^4
Derivada de 2x
Resolver d/dx 2x
Frequently Asked Questions
What is the derivative of x^4*atan(x)?▼
The derivative of x^4*atan(x) is (1+x^2)^(-1)*x^4+4*atan(x)*x^3.
How do you find the derivative of x^4*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^4+4*atan(x)*x^3.
Why is the derivative of x^4*atan(x) equal to (1+x^2)^(-1)*x^4+4*atan(x)*x^3?▼
Because differentiation measures how a function changes — applying the rules to x^4*atan(x) yields (1+x^2)^(-1)*x^4+4*atan(x)*x^3. See the full step-by-step breakdown above.