Derivative of 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)

The derivative of tan(9*x)*sec(9*x) is 9*cos(9*x)^(-1)*sec(9*x)^2+9*cos(9*x)^(-2)*sin(9*x)*tan(9*x).

Instant step-by-step solution for tan(9x)*sec(9x)

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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/derivative-of-tan9xsec9x

How to find the derivative of tan(9x)*sec(9x)

To find the derivative of tan(9x)*sec(9x), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

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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.

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