Derivada de tan(5x)*sec(5x)

Answer

5⋅sec(5⋅x)2cos(5⋅x)+5⋅sin(5⋅x)⋅tan(5⋅x)cos(5⋅x)2\frac{5 \cdot \mathrm{sec}\left(5 \cdot x\right)^{2}}{\mathrm{cos}\left(5 \cdot x\right)}+\frac{5 \cdot \mathrm{sin}\left(5 \cdot x\right) \cdot \mathrm{tan}\left(5 \cdot x\right)}{\mathrm{cos}\left(5 \cdot x\right)^{2}}
5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x)

Derivative of tan(5x)*sec(5x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(5⋅x)\tan(5 \cdot x)*sec⁡(5⋅x)\sec(5 \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: 5⋅c5 \cdot cos(5⋅x5 \cdot x)^(-1)*sec⁡(5⋅x)2\sec(5 \cdot x)^2+5⋅c5 \cdot cos(5⋅x5 \cdot x)^(-2)*sin⁡(5⋅x)\sin(5 \cdot x)*tan⁡(5⋅x)\tan(5 \cdot x)

La derivada de tan(5*x)*sec(5*x) es 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x).

Solución paso a paso instantánea para tan(5x)*sec(5x)

DerivativeTrigonometricIntermediate
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Derivative of tan(5x)*sec(5x) = 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-tan5xsec5x

Cómo encontrar la derivada de tan(5x)*sec(5x)

Para encontrar la derivada de tan(5x)*sec(5x), 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 tan(5x)*sec(5x)?▼
The derivative of tan(5x)*sec(5x) is 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x).
How do you find the derivative of tan(5x)*sec(5x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x).
Why is the derivative of tan(5x)*sec(5x) equal to 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(5x)*sec(5x) yields 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x). See the full step-by-step breakdown above.

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