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

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

Simplify

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

= cot (x)

y = 2 x + 1, (4, 3)

2 t^{- \frac{1}{4}}

\int \frac{x ^{2}}{e ^{\frac{x}{3}}} d x

5 \cdot t

\int \frac{1}{x ^{2} x ^{2} + 25} 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)