What is the derivative of (6x)/(1-cot(x)) ?

The derivative of (6x)/(1-cot(x)) is (6(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)

What is the first derivative of (6x)/(1-cot(x)) ?

The first derivative of (6x)/(1-cot(x)) is (6(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{6 x}{1 - cot ( x )}

\frac{6 ( 1 - cot ( x ) - x csc ^{2} ( x ) )}{( 1 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x}{1 - cot ( x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (\frac{x}{1 - cot ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 6 \cdot \frac{\frac{d x}{d x} ( 1 - cot ( x ) ) - \frac{d}{d x} ( 1 - cot ( x ) ) x}{( 1 - cot ( x ) ) ^{2}}

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

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

= 6 \cdot \frac{1 \cdot ( 1 - cot ( x ) ) - csc ^{2} ( x ) x}{( 1 - cot ( x ) ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot ( 1 - cot ( x ) ) - csc ^{2} ( x ) x}{( 1 - cot ( x ) ) ^{2}} : \frac{6 ( 1 - cot ( x ) - x csc ^{2} ( x ) )}{( 1 - cot ( x ) ) ^{2}}

= \frac{6 ( 1 - cot ( x ) - x csc ^{2} ( x ) )}{( 1 - cot ( x ) ) ^{2}}

\int \frac{( x + 1 ) ^{3}}{( x ) ^{10}} d x

\frac{x}{99}

\frac{d}{d X} (7.1 X + 20.3)

\frac{d}{d x} ((3 x^{2} - 3 x + 1) x^{3})

\int_{0}^{3} (3 - x) x d x

What is the derivative of (6x)/(1-cot(x)) ?
The derivative of (6x)/(1-cot(x)) is (6(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)
What is the first derivative of (6x)/(1-cot(x)) ?
The first derivative of (6x)/(1-cot(x)) is (6(1-cot(x)-xcsc^2(x)))/((1-cot(x))^2)