Derivada de e^(5x)*sin(3x)
Answer
3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x)
Derivative of e^(5x)*sin(3x)
- 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)*sin(3*x) é 3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x).
Solução passo a passo instantânea para e^(5x)*sin(3x)
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Derivative of e^(5x)*sin(3x) = 3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x) Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-e-minus-to-minus-the-minus-5xsin3x
Como encontrar a derivada de e^(5x)*sin(3x)
Para encontrar a derivada de e^(5x)*sin(3x), 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)*sin(3x)?▼
The derivative of e^(5x)*sin(3x) is 3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x).
How do you find the derivative of e^(5x)*sin(3x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x).
Why is the derivative of e^(5x)*sin(3x) equal to 3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(5x)*sin(3x) yields 3*e^(5*x)*cos(3*x)+5*e^(5*x)*sin(3*x). See the full step-by-step breakdown above.