Derivada de tan(10*x)*sec(10*x)

Answer

10⋅sec(10⋅x)2cos(10⋅x)+10⋅sin(10⋅x)⋅tan(10⋅x)cos(10⋅x)2\frac{10 \cdot \mathrm{sec}\left(10 \cdot x\right)^{2}}{\mathrm{cos}\left(10 \cdot x\right)}+\frac{10 \cdot \mathrm{sin}\left(10 \cdot x\right) \cdot \mathrm{tan}\left(10 \cdot x\right)}{\mathrm{cos}\left(10 \cdot x\right)^{2}}
10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x)

Derivative of tan(10*x)*sec(10*x)

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

A derivada de tan(10*x)*sec(10*x) é 10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x).

Solução passo a passo instantânea para tan(10*x)*sec(10*x)

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Derivative of tan(10*x)*sec(10*x) = 10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x) Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-tan10xsec10x

Como encontrar a derivada de tan(10*x)*sec(10*x)

Para encontrar a derivada de tan(10*x)*sec(10*x), 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(10*x)*sec(10*x)?▼
The derivative of tan(10*x)*sec(10*x) is 10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x).
How do you find the derivative of tan(10*x)*sec(10*x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x).
Why is the derivative of tan(10*x)*sec(10*x) equal to 10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(10*x)*sec(10*x) yields 10*cos(10*x)^(-1)*sec(10*x)^2+10*cos(10*x)^(-2)*sin(10*x)*tan(10*x). See the full step-by-step breakdown above.

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