Derivada de e^(5x)*cos(3x)
Answer
-3*e^(5*x)*sin(3*x)+5*e^(5*x)*cos(3*x)
Derivative of e^(5x)*cos(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^(5*x)*cos(3*x) es -3*e^(5*x)*sin(3*x)+5*e^(5*x)*cos(3*x).
Solución paso a paso instantánea para e^(5x)*cos(3x)
Share this result
Derivative of e^(5x)*cos(3x) = -3*e^(5*x)*sin(3*x)+5*e^(5*x)*cos(3*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-e-minus-to-minus-the-minus-5xcos3x
Cómo encontrar la derivada de e^(5x)*cos(3x)
Para encontrar la derivada de e^(5x)*cos(3x), usamos reglas de diferenciación estándar. Nuestra calculadora con IA desglosa los pasos y explica la lógica.
Practicar Más Problemas
Derivada de x*sin(x)
Resolver d/dx x*sin(x)
Derivada de x^2
Resolver d/dx x^2
Derivada de x^2-1
Resolver d/dx x^2-1
Derivada de x^2+1
Resolver d/dx x^2+1
Derivada de x^4
Resolver d/dx x^4
Derivada de 10^x
Resolver d/dx 10^x
Derivada de 2^x
Resolver d/dx 2^x
Derivada de e^(2x)
Resolver d/dx e^(2x)
Derivada de e^(-x)
Resolver d/dx e^(-x)
Derivada de e^x
Resolver d/dx e^x
Frequently Asked Questions
What is the derivative of e^(5x)*cos(3x)?▼
The derivative of e^(5x)*cos(3x) is -3*e^(5*x)*sin(3*x)+5*e^(5*x)*cos(3*x).
How do you find the derivative of e^(5x)*cos(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)*sin(3*x)+5*e^(5*x)*cos(3*x).
Why is the derivative of e^(5x)*cos(3x) equal to -3*e^(5*x)*sin(3*x)+5*e^(5*x)*cos(3*x)?▼
Because differentiation measures how a function changes — applying the rules to e^(5x)*cos(3x) yields -3*e^(5*x)*sin(3*x)+5*e^(5*x)*cos(3*x). See the full step-by-step breakdown above.