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

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

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

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

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

- cot (x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= \frac{1}{csc ( x )} (- cot (x) csc (x))

Simplify

\frac{1}{csc ( x )} (- cot (x) csc (x)) : - cot (x)

= - cot (x)

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