Derivada de x*e^(4x)
Answer
e^(4*x)+4*e^(4*x)*x
Derivative of x*e^(4x)
- Rule Used
- Product Rule
- Steps
- Identify a product of two functions of x in 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: +*x
A derivada de x*e^(4*x) é e^(4*x)+4*e^(4*x)*x.
Solução passo a passo instantânea para x*e^(4x)
Share this result
Derivative of x*e^(4x) = e^(4*x)+4*e^(4*x)*x Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-xe-minus-to-minus-the-minus-4x
Como encontrar a derivada de x*e^(4x)
Para encontrar a derivada de x*e^(4x), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a lógica.
Praticar Mais Problemas
Derivada de x^2+1
Resolver d/dx x^2+1
Derivada de x^4
Resolver d/dx x^4
Derivada de 10^x
Resolver d/dx 10^x
Derivada de 2^x
Resolver d/dx 2^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 x*e^x
Resolver d/dx x*e^x
Derivada de 1-x
Resolver d/dx 1-x
Derivada de 1/x
Resolver d/dx 1/x
Frequently Asked Questions
What is the derivative of x*e^(4x)?▼
The derivative of x*e^(4x) is e^(4*x)+4*e^(4*x)*x.
How do you find the derivative of x*e^(4x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is e^(4*x)+4*e^(4*x)*x.
Why is the derivative of x*e^(4x) equal to e^(4*x)+4*e^(4*x)*x?▼
Because differentiation measures how a function changes — applying the rules to x*e^(4x) yields e^(4*x)+4*e^(4*x)*x. See the full step-by-step breakdown above.