What is the d/(dt)(ln(sec(t))) ?

The d/(dt)(ln(sec(t))) is tan(t)

What is the first d/(dt)(ln(sec(t))) ?

The first d/(dt)(ln(sec(t))) is tan(t)

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\frac{d}{d t} (ln (sec (t)))

tan (t)

Solution steps

\frac{d}{d t} (ln (sec (t)))

Apply the chain rule:

\frac{1}{sec ( t )} \frac{d}{d t} (sec (t))

= \frac{1}{sec ( t )} \frac{d}{d t} (sec (t))

\frac{d}{d t} (sec (t)) = sec (t) tan (t)

= \frac{1}{sec ( t )} sec (t) tan (t)

Simplify

\frac{1}{sec ( t )} sec (t) tan (t) : tan (t)

= tan (t)

\frac{d ^{2}}{d x ^{2}} (x^{2} cos (x))

\int \frac{x}{( 3 x ^{2} - 1 )} d x

\int_{1}^{5} \frac{1}{x - 2} d x

n = 1 \sum \infty \frac{n}{1 + 3 n}

n = 1 \sum \infty \frac{1}{n ^{0.5}}