What is the derivative of sqrt(cot(3x)) ?

The derivative of sqrt(cot(3x)) is -(3csc^2(3x))/(2sqrt(cot(3x)))

What is the first derivative of sqrt(cot(3x)) ?

The first derivative of sqrt(cot(3x)) is -(3csc^2(3x))/(2sqrt(cot(3x)))

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derivative of

cot (3 x)

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 cot ( 3 x )} \frac{d}{d x} (cot (3 x))

= \frac{1}{2 cot ( 3 x )} \frac{d}{d x} (cot (3 x))

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

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

Simplify

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

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

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 6

ln (1 + x^{3})

\int - 5 csc^{2} (x) + 5 d x

\int (x e^{- x}) d x

What is the derivative of sqrt(cot(3x)) ?
The derivative of sqrt(cot(3x)) is -(3csc^2(3x))/(2sqrt(cot(3x)))
What is the first derivative of sqrt(cot(3x)) ?
The first derivative of sqrt(cot(3x)) is -(3csc^2(3x))/(2sqrt(cot(3x)))