Derivative of tan(8x)*sec(8x)

Answer

8⋅sec(8⋅x)2cos(8⋅x)+8⋅sin(8⋅x)⋅tan(8⋅x)cos(8⋅x)2\frac{8 \cdot \mathrm{sec}\left(8 \cdot x\right)^{2}}{\mathrm{cos}\left(8 \cdot x\right)}+\frac{8 \cdot \mathrm{sin}\left(8 \cdot x\right) \cdot \mathrm{tan}\left(8 \cdot x\right)}{\mathrm{cos}\left(8 \cdot x\right)^{2}}
8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x)

Derivative of tan(8x)*sec(8x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(8⋅x)\tan(8 \cdot x)*sec⁡(8⋅x)\sec(8 \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: 8⋅c8 \cdot cos(8⋅x8 \cdot x)^(-1)*sec⁡(8⋅x)2\sec(8 \cdot x)^2+8⋅c8 \cdot cos(8⋅x8 \cdot x)^(-2)*sin⁡(8⋅x)\sin(8 \cdot x)*tan⁡(8⋅x)\tan(8 \cdot x)

The derivative of tan(8*x)*sec(8*x) is 8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x).

Instant step-by-step solution for tan(8x)*sec(8x)

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Derivative of tan(8x)*sec(8x) = 8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-tan8xsec8x

How to find the derivative of tan(8x)*sec(8x)

To find the derivative of tan(8x)*sec(8x), 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(8x)*sec(8x)?▼
The derivative of tan(8x)*sec(8x) is 8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x).
How do you find the derivative of tan(8x)*sec(8x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x).
Why is the derivative of tan(8x)*sec(8x) equal to 8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(8x)*sec(8x) yields 8*cos(8*x)^(-1)*sec(8*x)^2+8*cos(8*x)^(-2)*sin(8*x)*tan(8*x). See the full step-by-step breakdown above.

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