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

Answer

\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}}

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

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $\tan(4 \cdot x)$ * $\sec(4 \cdot x)$ : 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.
Differentiate each factor and combine.
Final answer: $4 \cdot c$ os( $4 \cdot x$ )^(-1)* $\sec(4 \cdot x)^2$ + $4 \cdot c$ os( $4 \cdot x$ )^(-2)* $\sin(4 \cdot x)$ * $\tan(4 \cdot x)$

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

Solução passo a passo instantânea para tan(4x)*sec(4x)

Derivative TrigonometricIntermediate

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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/pt/derivative-of-tan4xsec4x

Como encontrar a derivada de tan(4x)*sec(4x)

Para encontrar a derivada de tan(4x)*sec(4x), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a 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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