What is the derivative of ln(cos(t)) ?

The derivative of ln(cos(t)) is -tan(t)

What is the first derivative of ln(cos(t)) ?

The first derivative of ln(cos(t)) is -tan(t)

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derivative of

ln (cos (t))

- tan (t)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d t} (cos (t)) = - sin (t)

= \frac{1}{cos ( t )} (- sin (t))

Simplify

\frac{1}{cos ( t )} (- sin (t)) : - tan (t)

= - tan (t)

\frac{d}{d x} ((x^{2} - 5 x)^{4})

n = 1 \sum \infty \frac{( ( - 1 ) ^{(n - 1)} )}{( ( 2 n - 1 ) ^{3} )}

\int \frac{x ^{2} - 4 x + 5}{( x ^{2} - 1 ) ( x + 3 )} d x

\int_{1}^{4} x ln (x) d x

\int sec (x) csc (x) d x

What is the derivative of ln(cos(t)) ?
The derivative of ln(cos(t)) is -tan(t)
What is the first derivative of ln(cos(t)) ?
The first derivative of ln(cos(t)) is -tan(t)