Derivada de sin(5x)*cos(5x)
Answer
-5*sin(5*x)^2+5*cos(5*x)^2
Derivative of sin(5x)*cos(5x)
- 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()^2+os()^2
La derivada de sin(5*x)*cos(5*x) es -5*sin(5*x)^2+5*cos(5*x)^2.
Solución paso a paso instantánea para sin(5x)*cos(5x)
Share this result
Derivative of sin(5x)*cos(5x) = -5*sin(5*x)^2+5*cos(5*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-sin5xcos5x
Cómo encontrar la derivada de sin(5x)*cos(5x)
Para encontrar la derivada de sin(5x)*cos(5x), 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 sin(5x)*cos(5x)?▼
The derivative of sin(5x)*cos(5x) is -5*sin(5*x)^2+5*cos(5*x)^2.
How do you find the derivative of sin(5x)*cos(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -5*sin(5*x)^2+5*cos(5*x)^2.
Why is the derivative of sin(5x)*cos(5x) equal to -5*sin(5*x)^2+5*cos(5*x)^2?▼
Because differentiation measures how a function changes — applying the rules to sin(5x)*cos(5x) yields -5*sin(5*x)^2+5*cos(5*x)^2. See the full step-by-step breakdown above.