Derivative of tan(7x)*sec(7x)

Answer

7⋅sec(7⋅x)2cos(7⋅x)+7⋅sin(7⋅x)⋅tan(7⋅x)cos(7⋅x)2\frac{7 \cdot \mathrm{sec}\left(7 \cdot x\right)^{2}}{\mathrm{cos}\left(7 \cdot x\right)}+\frac{7 \cdot \mathrm{sin}\left(7 \cdot x\right) \cdot \mathrm{tan}\left(7 \cdot x\right)}{\mathrm{cos}\left(7 \cdot x\right)^{2}}
7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x)

Derivative of tan(7x)*sec(7x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(7⋅x)\tan(7 \cdot x)*sec⁡(7⋅x)\sec(7 \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: 7⋅c7 \cdot cos(7⋅x7 \cdot x)^(-1)*sec⁡(7⋅x)2\sec(7 \cdot x)^2+7⋅c7 \cdot cos(7⋅x7 \cdot x)^(-2)*sin⁡(7⋅x)\sin(7 \cdot x)*tan⁡(7⋅x)\tan(7 \cdot x)

The derivative of tan(7*x)*sec(7*x) is 7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x).

Instant step-by-step solution for tan(7x)*sec(7x)

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Derivative of tan(7x)*sec(7x) = 7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-tan7xsec7x

How to find the derivative of tan(7x)*sec(7x)

To find the derivative of tan(7x)*sec(7x), 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(7x)*sec(7x)?▼
The derivative of tan(7x)*sec(7x) is 7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x).
How do you find the derivative of tan(7x)*sec(7x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x).
Why is the derivative of tan(7x)*sec(7x) equal to 7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(7x)*sec(7x) yields 7*cos(7*x)^(-1)*sec(7*x)^2+7*cos(7*x)^(-2)*sin(7*x)*tan(7*x). See the full step-by-step breakdown above.

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