Derivada de e^(3x)*sin(5x)

Answer

3⋅3253681253⋅x⋅sin(5⋅x)1196962443⋅x+5⋅3253681253⋅x⋅cos(5⋅x)1196962443⋅x\frac{3 \cdot 325368125^{3 \cdot x} \cdot \mathrm{sin}\left(5 \cdot x\right)}{119696244^{3 \cdot x}}+\frac{5 \cdot 325368125^{3 \cdot x} \cdot \mathrm{cos}\left(5 \cdot x\right)}{119696244^{3 \cdot x}}
3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x)

Derivative of e^(3x)*sin(5x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in e3⋅xe^{3 \cdot x}*sin⁡(5⋅x)\sin(5 \cdot 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.
  2. Differentiate each factor and combine.
  3. Final answer: 3⋅e3⋅x3 \cdot e^{3 \cdot x}*sin⁡(5⋅x)\sin(5 \cdot x)+5⋅e3⋅x5 \cdot e^{3 \cdot x}*cos⁡(5⋅x)\cos(5 \cdot x)

La derivada de e^(3*x)*sin(5*x) es 3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x).

Solución paso a paso instantánea para e^(3x)*sin(5x)

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Derivative of e^(3x)*sin(5x) = 3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-e-minus-to-minus-the-minus-3xsin5x

Cómo encontrar la derivada de e^(3x)*sin(5x)

Para encontrar la derivada de e^(3x)*sin(5x), 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^(3x)*sin(5x)?▼
The derivative of e^(3x)*sin(5x) is 3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x).
How do you find the derivative of e^(3x)*sin(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x).
Why is the derivative of e^(3x)*sin(5x) equal to 3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(3x)*sin(5x) yields 3*e^(3*x)*sin(5*x)+5*e^(3*x)*cos(5*x). See the full step-by-step breakdown above.

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