Derivada de e^(3x)*sin(4x)

Answer

\frac{3 \cdot 325368125^{3 \cdot x} \cdot \mathrm{sin}\left(4 \cdot x\right)}{119696244^{3 \cdot x}}+\frac{4 \cdot 325368125^{3 \cdot x} \cdot \mathrm{cos}\left(4 \cdot x\right)}{119696244^{3 \cdot x}}

Derivative of e^(3x)*sin(4x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $e^{3 \cdot x}$ * $\sin(4 \cdot x)$ : 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.
Differentiate each factor and combine.
Final answer: $3 \cdot e^{3 \cdot x}$ * $\sin(4 \cdot x)$ + $4 \cdot e^{3 \cdot x}$ * $\cos(4 \cdot x)$

La derivada de e^(3*x)*sin(4*x) es 3*e^(3*x)*sin(4*x)+4*e^(3*x)*cos(4*x).

Solución paso a paso instantánea para e^(3x)*sin(4x)

Derivative ExponentialIntermediate

Share this result

Share on X

Derivative of e^(3x)*sin(4x) = 3*e^(3*x)*sin(4*x)+4*e^(3*x)*cos(4*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-e-minus-to-minus-the-minus-3xsin4x

Cómo encontrar la derivada de e^(3x)*sin(4x)

Para encontrar la derivada de e^(3x)*sin(4x), usamos reglas de diferenciación estándar. Nuestra calculadora con IA desglosa los pasos y explica la lógica.

Practicar Más Problemas

Derivada de sin(x)

Resolver d/dx sin(x)

Derivada de sinh(x)

Resolver d/dx sinh(x)

Derivada de sqrt(x)

Resolver d/dx sqrt(x)

Derivada de tan(x)^2

Resolver d/dx tan(x)^2

Derivada de tan(x)

Resolver d/dx tan(x)

Derivada de tanh(x)

Resolver d/dx tanh(x)

Derivada de x*cos(x)

Resolver d/dx x*cos(x)

Derivada de x^3

Resolver d/dx x^3

Derivada de x*ln(x)

Resolver d/dx x*ln(x)

Derivada de x+1

Resolver d/dx x+1

Frequently Asked Questions

What is the derivative of e^(3x)*sin(4x)?▼

The derivative of e^(3x)*sin(4x) is 3*e^(3*x)*sin(4*x)+4*e^(3*x)*cos(4*x).

How do you find the derivative of e^(3x)*sin(4x)?▼

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(4*x)+4*e^(3*x)*cos(4*x).

Why is the derivative of e^(3x)*sin(4x) equal to 3*e^(3*x)*sin(4*x)+4*e^(3*x)*cos(4*x)?▼

Because differentiation measures how a function changes — applying the rules to e^(3x)*sin(4x) yields 3*e^(3*x)*sin(4*x)+4*e^(3*x)*cos(4*x). See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️