Derivada de sin(10*x)*cos(10*x)

Answer

−10⋅sin(10⋅x)2+10⋅cos(10⋅x)2-10 \cdot \mathrm{sin}\left(10 \cdot x\right)^{2}+10 \cdot \mathrm{cos}\left(10 \cdot x\right)^{2}
-10*sin(10*x)^2+10*cos(10*x)^2

Derivative of sin(10*x)*cos(10*x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in sin⁡(10⋅x)\sin(10 \cdot x)*cos⁡(10⋅x)\cos(10 \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: -10⋅s10 \cdot sin(10⋅x10 \cdot x)^2+10⋅c10 \cdot cos(10⋅x10 \cdot x)^2

La derivada de sin(10*x)*cos(10*x) es -10*sin(10*x)^2+10*cos(10*x)^2.

Solución paso a paso instantánea para sin(10*x)*cos(10*x)

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Derivative of sin(10*x)*cos(10*x) = -10*sin(10*x)^2+10*cos(10*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-sin10xcos10x

Cómo encontrar la derivada de sin(10*x)*cos(10*x)

Para encontrar la derivada de sin(10*x)*cos(10*x), 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 sin(10*x)*cos(10*x)?▼
The derivative of sin(10*x)*cos(10*x) is -10*sin(10*x)^2+10*cos(10*x)^2.
How do you find the derivative of sin(10*x)*cos(10*x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -10*sin(10*x)^2+10*cos(10*x)^2.
Why is the derivative of sin(10*x)*cos(10*x) equal to -10*sin(10*x)^2+10*cos(10*x)^2?▼
Because differentiation measures how a function changes — applying the rules to sin(10*x)*cos(10*x) yields -10*sin(10*x)^2+10*cos(10*x)^2. See the full step-by-step breakdown above.

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