Derivada de e^(3x)*cos(5x)
Answer
-5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x)
Derivative of e^(3x)*cos(5x)
- 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^(3*x)*cos(5*x) é -5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x).
Solução passo a passo instantânea para e^(3x)*cos(5x)
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Derivative of e^(3x)*cos(5x) = -5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-e-minus-to-minus-the-minus-3xcos5x
Como encontrar a derivada de e^(3x)*cos(5x)
Para encontrar a derivada de e^(3x)*cos(5x), 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^(3x)*cos(5x)?▼
The derivative of e^(3x)*cos(5x) is -5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x).
How do you find the derivative of e^(3x)*cos(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x).
Why is the derivative of e^(3x)*cos(5x) equal to -5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(3x)*cos(5x) yields -5*e^(3*x)*sin(5*x)+3*e^(3*x)*cos(5*x). See the full step-by-step breakdown above.