Derivative of tan(3x)*sec(3x)

Answer

3⋅sec(3⋅x)2cos(3⋅x)+3⋅sin(3⋅x)⋅tan(3⋅x)cos(3⋅x)2\frac{3 \cdot \mathrm{sec}\left(3 \cdot x\right)^{2}}{\mathrm{cos}\left(3 \cdot x\right)}+\frac{3 \cdot \mathrm{sin}\left(3 \cdot x\right) \cdot \mathrm{tan}\left(3 \cdot x\right)}{\mathrm{cos}\left(3 \cdot x\right)^{2}}
3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x)

Derivative of tan(3x)*sec(3x)

Rule Used
Product Rule
Steps
  1. Identify a product of two functions of x in tan⁡(3⋅x)\tan(3 \cdot x)*sec⁡(3⋅x)\sec(3 \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: 3⋅c3 \cdot cos(3⋅x3 \cdot x)^(-1)*sec⁡(3⋅x)2\sec(3 \cdot x)^2+3⋅c3 \cdot cos(3⋅x3 \cdot x)^(-2)*sin⁡(3⋅x)\sin(3 \cdot x)*tan⁡(3⋅x)\tan(3 \cdot x)

The derivative of tan(3*x)*sec(3*x) is 3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x).

Instant step-by-step solution for tan(3x)*sec(3x)

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Derivative of tan(3x)*sec(3x) = 3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-tan3xsec3x

How to find the derivative of tan(3x)*sec(3x)

To find the derivative of tan(3x)*sec(3x), 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(3x)*sec(3x)?▼
The derivative of tan(3x)*sec(3x) is 3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x).
How do you find the derivative of tan(3x)*sec(3x)?▼
Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x).
Why is the derivative of tan(3x)*sec(3x) equal to 3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x)?▼
Because differentiation measures how a function changes — applying the rules to tan(3x)*sec(3x) yields 3*cos(3*x)^(-1)*sec(3*x)^2+3*cos(3*x)^(-2)*sin(3*x)*tan(3*x). See the full step-by-step breakdown above.

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