Derivada de e^(5x)*cos(2x)
Answer
-2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x)
Derivative of e^(5x)*cos(2x)
- 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: -*+*
A derivada de e^(5*x)*cos(2*x) é -2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x).
Solução passo a passo instantânea para e^(5x)*cos(2x)
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Derivative of e^(5x)*cos(2x) = -2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x) Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-e-minus-to-minus-the-minus-5xcos2x
Como encontrar a derivada de e^(5x)*cos(2x)
Para encontrar a derivada de e^(5x)*cos(2x), 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 e^(5x)*cos(2x)?▼
The derivative of e^(5x)*cos(2x) is -2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x).
How do you find the derivative of e^(5x)*cos(2x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x).
Why is the derivative of e^(5x)*cos(2x) equal to -2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(5x)*cos(2x) yields -2*e^(5*x)*sin(2*x)+5*e^(5*x)*cos(2*x). See the full step-by-step breakdown above.