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Popular >

derivative of ln|sec(x|)

Solution

\frac{d}{d x} (ln ∣ sec (x) ∣)

Solution

tan (x)

Solution steps

\frac{d}{d x} (ln ∣ sec (x) ∣)

Apply the chain rule:

\frac{1}{∣ sec ( x ) ∣} \frac{d}{d x} (∣ sec (x) ∣)

= \frac{1}{∣ sec ( x ) ∣} \frac{d}{d x} (∣ sec (x) ∣)

\frac{d}{d x} (∣ sec (x) ∣) = \frac{sec ^{2} ( x ) tan ( x )}{∣ sec ( x ) ∣}

= \frac{1}{∣ sec ( x ) ∣} \cdot \frac{sec ^{2} ( x ) tan ( x )}{∣ sec ( x ) ∣}

Simplify

\frac{1}{∣ sec ( x ) ∣} \cdot \frac{sec ^{2} ( x ) tan ( x )}{∣ sec ( x ) ∣} : tan (x)

= tan (x)

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Frequently Asked Questions (FAQ)

What is the derivative of ln|sec(x|) ?
The derivative of ln|sec(x|) is tan(x)
What is the first derivative of ln|sec(x|) ?
The first derivative of ln|sec(x|) is tan(x)