What is the derivative of (2x/(3-cot(x))) ?

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

What is the first derivative of (2x/(3-cot(x))) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

5^{2 x + 6} (ln (5 x + 7))

\int 9 x^{2} - 1 d x

f (x) = 4 sec (x)

(ln (6 x))^{11}

x \to 5 - lim (\frac{x}{x + 1})

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