What is the derivative of (8x)/(5-cot(x)) ?

The derivative of (8x)/(5-cot(x)) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)

What is the first derivative of (8x)/(5-cot(x)) ?

The first derivative of (8x)/(5-cot(x)) is (8(5-cot(x)-xcsc^2(x)))/((5-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{8 x}{5 - cot ( x )}

\frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x}{5 - cot ( x )})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{x}{5 - cot ( x )})

Apply the Quotient Rule:

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

= 8 \cdot \frac{\frac{d x}{d x} ( 5 - cot ( x ) ) - \frac{d}{d x} ( 5 - cot ( x ) ) x}{( 5 - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (5 - cot (x)) = csc^{2} (x)

= 8 \cdot \frac{1 \cdot ( 5 - cot ( x ) ) - csc ^{2} ( x ) x}{( 5 - cot ( x ) ) ^{2}}

Simplify

8 \cdot \frac{1 \cdot ( 5 - cot ( x ) ) - csc ^{2} ( x ) x}{( 5 - cot ( x ) ) ^{2}} : \frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

= \frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

\frac{d}{d x} (x arccos (\frac{1}{x}))

\int a e^{- b x} d x

\frac{d y}{d x} = y (1 - 0.0008 y)

\frac{d}{d x} (9 x + 7)

6 y^{^{''}} - 6 y^{^{'}} + 39 y = 0

What is the derivative of (8x)/(5-cot(x)) ?
The derivative of (8x)/(5-cot(x)) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)
What is the first derivative of (8x)/(5-cot(x)) ?
The first derivative of (8x)/(5-cot(x)) is (8(5-cot(x)-xcsc^2(x)))/((5-cot(x))^2)