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