Derivada de e^(6x)*sin(3x)
Answer
3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x)
Derivative of e^(6x)*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: *+*
La derivada de e^(6*x)*sin(3*x) es 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x).
Solución paso a paso instantánea para e^(6x)*sin(3x)
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Derivative of e^(6x)*sin(3x) = 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-e-minus-to-minus-the-minus-6xsin3x
Cómo encontrar la derivada de e^(6x)*sin(3x)
Para encontrar la derivada de e^(6x)*sin(3x), usamos reglas de diferenciación estándar. Nuestra calculadora con IA desglosa los pasos y explica la lógica.
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Frequently Asked Questions
What is the derivative of e^(6x)*sin(3x)?▼
The derivative of e^(6x)*sin(3x) is 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x).
How do you find the derivative of e^(6x)*sin(3x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x).
Why is the derivative of e^(6x)*sin(3x) equal to 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(6x)*sin(3x) yields 3*e^(6*x)*cos(3*x)+6*e^(6*x)*sin(3*x). See the full step-by-step breakdown above.