What is the derivative of ln(cot(5x)) ?

The derivative of ln(cot(5x)) is -5csc^2(5x)tan(5x)

What is the first derivative of ln(cot(5x)) ?

The first derivative of ln(cot(5x)) is -5csc^2(5x)tan(5x)

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\frac{d}{d x} (ln (cot (5 x)))

- 5 csc^{2} (5 x) tan (5 x)

Solution steps

\frac{d}{d x} (ln (cot (5 x)))

Apply the chain rule:

\frac{1}{cot ( 5 x )} \frac{d}{d x} (cot (5 x))

= \frac{1}{cot ( 5 x )} \frac{d}{d x} (cot (5 x))

\frac{d}{d x} (cot (5 x)) = - csc^{2} (5 x) \cdot 5

= \frac{1}{cot ( 5 x )} (- csc^{2} (5 x) \cdot 5)

Simplify

\frac{1}{cot ( 5 x )} (- csc^{2} (5 x) \cdot 5) : - 5 csc^{2} (5 x) tan (5 x)

= - 5 csc^{2} (5 x) tan (5 x)

f (x) = 4 x^{2} - 4 x + 1

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (x)

\int \frac{1}{2 y - 1} d y

n = 0 \sum \infty 0. 9^{n}

\int tan^{7} (x) sec^{2} (x) d x

What is the derivative of ln(cot(5x)) ?
The derivative of ln(cot(5x)) is -5csc^2(5x)tan(5x)
What is the first derivative of ln(cot(5x)) ?
The first derivative of ln(cot(5x)) is -5csc^2(5x)tan(5x)