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

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

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

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

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

sec (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= sec (x)

\int cos^{2} (2 u) d u

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x \to 0 lim (e^{3 x} - 1)

\int 4 x e^{- 2 x} d x

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