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

The derivative of ln(sin(t)) is cot(t)

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

The first derivative of ln(sin(t)) is cot(t)

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derivative of

ln (sin (t))

cot (t)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{sin ( t )} cos (t) : cot (t)

= cot (t)

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

\frac{\partial}{\partial x} ((x + 10)^{2} \cdot (y + 2))

f (x) = \frac{x ^{3}}{3} + \frac{3}{x ^{3}}

\int x 5^{- x} d x

\int x (2 x + 5) d x

What is the derivative of ln(sin(t)) ?
The derivative of ln(sin(t)) is cot(t)
What is the first derivative of ln(sin(t)) ?
The first derivative of ln(sin(t)) is cot(t)