What is the derivative of f(x)=ln|cot(3*x)| ?

The derivative of f(x)=ln|cot(3*x)| is -3csc^2(3x)tan(3x)

What is the first derivative of f(x)=ln|cot(3*x)| ?

The first derivative of f(x)=ln|cot(3*x)| is -3csc^2(3x)tan(3x)

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derivative of

f (x) = ln ∣ cot (3 \cdot x) ∣

- 3 csc^{2} (3 x) tan (3 x)

Solution steps

\frac{d}{d x} (ln ∣ cot (3 x) ∣)

Apply the chain rule:

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

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

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

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

Simplify

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

= - 3 csc^{2} (3 x) tan (3 x)

((3 x^{2} + 3 x + 4)^{^{'}} (3 x^{2} + 6 x)^{^{'}})^{^{'}}

\int e^{t a n (2 x)} sec^{2} (2 x) d x

\int \frac{1}{3 x ^{4}} d x

\int_{- 1}^{1} \frac{1}{2} (4 - 4 x^{2})^{2} d x

\frac{\partial}{\partial t} (\frac{s - 3 r}{t})

What is the derivative of f(x)=ln|cot(3*x)| ?
The derivative of f(x)=ln|cot(3*x)| is -3csc^2(3x)tan(3x)
What is the first derivative of f(x)=ln|cot(3*x)| ?
The first derivative of f(x)=ln|cot(3*x)| is -3csc^2(3x)tan(3x)