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Popular >

derivative of ln(sec(x+tan(x)))

Solution

\frac{d}{d x} (ln (sec (x) + tan (x)))

Solution

sec (x)

Solution steps

\frac{d}{d x} (ln (sec (x) + tan (x)))

Apply the chain rule:

\frac{1}{sec ( x ) + tan ( x )} \frac{d}{d x} (sec (x) + tan (x))

= \frac{1}{sec ( x ) + tan ( x )} \frac{d}{d x} (sec (x) + tan (x))

\frac{d}{d x} (sec (x) + tan (x)) = - \frac{1}{- 1 + sin ( x )}

= \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )})

Simplify

\frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )}) : sec (x)

= sec (x)

Graph

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Frequently Asked Questions (FAQ)

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