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

The derivative of ln(cot(x)) is -csc^2(x)tan(x)

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

The first derivative of ln(cot(x)) is -csc^2(x)tan(x)

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

- csc^{2} (x) tan (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - csc^{2} (x) tan (x)

x \to - 5 - lim (x^{2} + \frac{4}{x + 5})

x \to 2 lim (\frac{x ^{4} - 9}{x + 2})

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 4 ) ^{2}})

f (x) = \frac{1}{x + 8}, at x = 9

n = 2 \sum \infty \frac{1}{n ^{3}}

What is the derivative of ln(cot(x)) ?
The derivative of ln(cot(x)) is -csc^2(x)tan(x)
What is the first derivative of ln(cot(x)) ?
The first derivative of ln(cot(x)) is -csc^2(x)tan(x)