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

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

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

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

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derivative of

ln (sin (x))

cot (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= cot (x)

y^{^{'}} = y x^{2}

t^{3} cos (3 t)

\frac{d}{d x} (1 + (x)^{2})

\int x 9^{x} d x

\int \frac{1}{26 - x ^{2}} d x

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