Derivada de tan(4x)*sec(4x)

Answer

4⋅sec(4⋅x)2cos(4⋅x)+4⋅sin(4⋅x)⋅tan(4⋅x)cos(4⋅x)2\frac{4 \cdot \mathrm{sec}\left(4 \cdot x\right)^{2}}{\mathrm{cos}\left(4 \cdot x\right)}+\frac{4 \cdot \mathrm{sin}\left(4 \cdot x\right) \cdot \mathrm{tan}\left(4 \cdot x\right)}{\mathrm{cos}\left(4 \cdot x\right)^{2}}
4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x)

Derivative of tan(4x)*sec(4x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(4⋅x)\tan(4 \cdot x)*sec⁡(4⋅x)\sec(4 \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: 4⋅c4 \cdot cos(4⋅x4 \cdot x)^(-1)*sec⁡(4⋅x)2\sec(4 \cdot x)^2+4⋅c4 \cdot cos(4⋅x4 \cdot x)^(-2)*sin⁡(4⋅x)\sin(4 \cdot x)*tan⁡(4⋅x)\tan(4 \cdot x)

La derivada de tan(4*x)*sec(4*x) es 4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x).

Solución paso a paso instantánea para tan(4x)*sec(4x)

DerivativeTrigonometricIntermediate
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Derivative of tan(4x)*sec(4x) = 4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-tan4xsec4x

Cómo encontrar la derivada de tan(4x)*sec(4x)

Para encontrar la derivada de tan(4x)*sec(4x), 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(4x)*sec(4x)?▼
The derivative of tan(4x)*sec(4x) is 4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x).
How do you find the derivative of tan(4x)*sec(4x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x).
Why is the derivative of tan(4x)*sec(4x) equal to 4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(4x)*sec(4x) yields 4*cos(4*x)^(-1)*sec(4*x)^2+4*cos(4*x)^(-2)*sin(4*x)*tan(4*x). See the full step-by-step breakdown above.

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