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)

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

- 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)) = sec (x) tan (x) - sec^{2} (x)

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

Simplify

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

= - sec (x)

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)