Derivative of tan(5x)*sec(5x)

Answer

\frac{5 \cdot \mathrm{sec}\left(5 \cdot x\right)^{2}}{\mathrm{cos}\left(5 \cdot x\right)}+\frac{5 \cdot \mathrm{sin}\left(5 \cdot x\right) \cdot \mathrm{tan}\left(5 \cdot x\right)}{\mathrm{cos}\left(5 \cdot x\right)^{2}}

Derivative of tan(5x)*sec(5x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $\tan(5 \cdot x)$ * $\sec(5 \cdot x)$ : 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.
Differentiate each factor and combine.
Final answer: $5 \cdot c$ os( $5 \cdot x$ )^(-1)* $\sec(5 \cdot x)^2$ + $5 \cdot c$ os( $5 \cdot x$ )^(-2)* $\sin(5 \cdot x)$ * $\tan(5 \cdot x)$

The derivative of tan(5*x)*sec(5*x) is 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x).

Instant step-by-step solution for tan(5x)*sec(5x)

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Derivative of tan(5x)*sec(5x) = 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-tan5xsec5x

How to find the derivative of tan(5x)*sec(5x)

To find the derivative of tan(5x)*sec(5x), 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(5x)*sec(5x)?▼

The derivative of tan(5x)*sec(5x) is 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x).

How do you find the derivative of tan(5x)*sec(5x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x).

Why is the derivative of tan(5x)*sec(5x) equal to 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x)?▼

Because differentiation measures how a function changes — applying the rules to tan(5x)*sec(5x) yields 5*cos(5*x)^(-1)*sec(5*x)^2+5*cos(5*x)^(-2)*sin(5*x)*tan(5*x). See the full step-by-step breakdown above.

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