Derivada de 1/(x^5+1)
Answer
-5*(1+x^5)^(-2)*x^4
Derivative of 1/(x^5+1)
- Rule Used
- Quotient Rule
- Steps
- Identify a quotient in 1/(+1): use the quotient rule (u/v)' = (u'v − uv')/v². The minus sign belongs to the derivative of the denominator; swapping it is the usual error.
- Differentiate numerator and denominator, then combine.
- Final answer: -5*(1+)^(-2)*
A derivada de 1/(x^5+1) é -5*(1+x^5)^(-2)*x^4.
Solução passo a passo instantânea para 1/(x^5+1)
Share this result
Derivative of 1/(x^5+1) = -5*(1+x^5)^(-2)*x^4 Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-1-minus-over-minus-x-minus-to-minus-the-minus-5-minus-plus-minus-1
Como encontrar a derivada de 1/(x^5+1)
Para encontrar a derivada de 1/(x^5+1), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a lógica.
Praticar Mais Problemas
Derivada de cos(x)
Resolver d/dx cos(x)
Derivada de cosh(x)
Resolver d/dx cosh(x)
Derivada de cot(x)
Resolver d/dx cot(x)
Derivada de csc(x)
Resolver d/dx csc(x)
Derivada de e^(2x)
Resolver d/dx e^(2x)
Derivada de e^(-x)
Resolver d/dx e^(-x)
Derivada de e^x
Resolver d/dx e^x
Derivada de ln(2x)
Resolver d/dx ln(2x)
Derivada de ln(x)
Resolver d/dx ln(x)
Frequently Asked Questions
What is the derivative of 1/(x^5+1)?▼
The derivative of 1/(x^5+1) is -5*(1+x^5)^(-2)*x^4.
How do you find the derivative of 1/(x^5+1)?▼
Apply the standard differentiation rules — the key rule used here is the Quotient Rule. The step-by-step result is -5*(1+x^5)^(-2)*x^4.
Why is the derivative of 1/(x^5+1) equal to -5*(1+x^5)^(-2)*x^4?▼
Because differentiation measures how a function changes — applying the rules to 1/(x^5+1) yields -5*(1+x^5)^(-2)*x^4. See the full step-by-step breakdown above.