What is the derivative of ln|csc(3x|) ?

The derivative of ln|csc(3x|) is -3cot(3x)

What is the first derivative of ln|csc(3x|) ?

The first derivative of ln|csc(3x|) is -3cot(3x)

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\frac{d}{d x} (ln ∣ csc (3 x) ∣)

- 3 cot (3 x)

Solution steps

\frac{d}{d x} (ln ∣ csc (3 x) ∣)

Apply the chain rule:

\frac{1}{∣ csc ( 3 x ) ∣} \frac{d}{d x} (∣ csc (3 x) ∣)

= \frac{1}{∣ csc ( 3 x ) ∣} \frac{d}{d x} (∣ csc (3 x) ∣)

\frac{d}{d x} (∣ csc (3 x) ∣) = - \frac{3 csc ^{2} ( 3 x ) cot ( 3 x )}{∣ csc ( 3 x ) ∣}

= \frac{1}{∣ csc ( 3 x ) ∣} (- \frac{3 csc ^{2} ( 3 x ) cot ( 3 x )}{∣ csc ( 3 x ) ∣})

Simplify

\frac{1}{∣ csc ( 3 x ) ∣} (- \frac{3 csc ^{2} ( 3 x ) cot ( 3 x )}{∣ csc ( 3 x ) ∣}) : - 3 cot (3 x)

= - 3 cot (3 x)

\int 4 e^{- 0.4 x} d x

\frac{∣ x ∣}{5 - x ^{2}}

\frac{d}{d x} (6 - e^{- x})

\frac{d y}{d x} = 7 y e^{x + 3}

What is the derivative of ln|csc(3x|) ?
The derivative of ln|csc(3x|) is -3cot(3x)
What is the first derivative of ln|csc(3x|) ?
The first derivative of ln|csc(3x|) is -3cot(3x)