What is the derivative of x/(tan(3x-1)) ?

The derivative of x/(tan(3x-1)) is cot(3x-1)-3xcsc^2(3x-1)

What is the first derivative of x/(tan(3x-1)) ?

The first derivative of x/(tan(3x-1)) is cot(3x-1)-3xcsc^2(3x-1)

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\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})

cot (3 x - 1) - 3 x csc^{2} (3 x - 1)

Solution steps

\frac{d}{d x} (\frac{x}{tan ( 3 x - 1 )})

Simplify

\frac{x}{tan ( 3 x - 1 )} : x cot (3 x - 1)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cot (3 x - 1)

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\int \frac{ln ( y )}{x y} d y

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

\frac{\partial}{\partial x} (x - 2 x - \frac{2}{3} y)

f (x) = x^{4} + 3 x

\frac{1}{1 - 2 x}

What is the derivative of x/(tan(3x-1)) ?
The derivative of x/(tan(3x-1)) is cot(3x-1)-3xcsc^2(3x-1)
What is the first derivative of x/(tan(3x-1)) ?
The first derivative of x/(tan(3x-1)) is cot(3x-1)-3xcsc^2(3x-1)