Derivada de tan(9x)*sec(9x)

Answer

9⋅sec(9⋅x)2cos(9⋅x)+9⋅sin(9⋅x)⋅tan(9⋅x)cos(9⋅x)2\frac{9 \cdot \mathrm{sec}\left(9 \cdot x\right)^{2}}{\mathrm{cos}\left(9 \cdot x\right)}+\frac{9 \cdot \mathrm{sin}\left(9 \cdot x\right) \cdot \mathrm{tan}\left(9 \cdot x\right)}{\mathrm{cos}\left(9 \cdot x\right)^{2}}
9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x)

Derivative of tan(9x)*sec(9x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(9⋅x)\tan(9 \cdot x)*sec⁡(9⋅x)\sec(9 \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: 9⋅c9 \cdot cos(9⋅x9 \cdot x)^(-1)*sec⁡(9⋅x)2\sec(9 \cdot x)^2+9⋅c9 \cdot cos(9⋅x9 \cdot x)^(-2)*sin⁡(9⋅x)\sin(9 \cdot x)*tan⁡(9⋅x)\tan(9 \cdot x)

La derivada de tan(9*x)*sec(9*x) es 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x).

Solución paso a paso instantánea para tan(9x)*sec(9x)

DerivativeTrigonometricIntermediate
Share this result
Share on X

Derivative of tan(9x)*sec(9x) = 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x) Solve step-by-step for free: https://derivativecalculatorai.com/es/derivative-of-tan9xsec9x

Cómo encontrar la derivada de tan(9x)*sec(9x)

Para encontrar la derivada de tan(9x)*sec(9x), usamos reglas de diferenciación estándar. Nuestra calculadora con IA desglosa los pasos y explica la lógica.

Practicar Más Problemas

Derivada de x*e^x
Resolver d/dx x*e^x
Derivada de x*ln(x)
Resolver d/dx x*ln(x)
Derivada de x+1
Resolver d/dx x+1
Derivada de x^2
Resolver d/dx x^2
Derivada de x^2-1
Resolver d/dx x^2-1
Derivada de x^2+1
Resolver d/dx x^2+1
Derivada de x^4
Resolver d/dx x^4
Derivada de cos(2x)
Resolver d/dx cos(2x)
Derivada de cos(x)^2
Resolver d/dx cos(x)^2
Derivada de cos(x)
Resolver d/dx cos(x)

Frequently Asked Questions

What is the derivative of tan(9x)*sec(9x)?▼
The derivative of tan(9x)*sec(9x) is 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x).
How do you find the derivative of tan(9x)*sec(9x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x).
Why is the derivative of tan(9x)*sec(9x) equal to 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(9x)*sec(9x) yields 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x). See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️