What is the derivative of (8x/(9-cot(x))) ?

The derivative of (8x/(9-cot(x))) is (8(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)

What is the first derivative of (8x/(9-cot(x))) ?

The first derivative of (8x/(9-cot(x))) is (8(9-cot(x)-xcsc^2(x)))/((9-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{8 x}{9 - cot ( x )})

\frac{8 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x}{9 - cot ( x )})

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{x}{9 - 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} ( 9 - cot ( x ) ) - \frac{d}{d x} ( 9 - cot ( x ) ) x}{( 9 - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (9 - cot (x)) = csc^{2} (x)

= 8 \cdot \frac{1 \cdot ( 9 - cot ( x ) ) - csc ^{2} ( x ) x}{( 9 - cot ( x ) ) ^{2}}

Simplify

8 \cdot \frac{1 \cdot ( 9 - cot ( x ) ) - csc ^{2} ( x ) x}{( 9 - cot ( x ) ) ^{2}} : \frac{8 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

= \frac{8 ( 9 - cot ( x ) - x csc ^{2} ( x ) )}{( 9 - cot ( x ) ) ^{2}}

x^{2} y^{^{''}} + 7 x y^{^{'}} + 8 y = 0, y (1) = 0, y^{^{'}} (1) = - 5

\frac{\partial}{\partial y} (ln (2 x + 3 y))

\frac{d}{d x} (\frac{x ^{3}}{2} + \frac{1}{6 x})

x^{2} + 2 x - 6

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

What is the derivative of (8x/(9-cot(x))) ?
The derivative of (8x/(9-cot(x))) is (8(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)
What is the first derivative of (8x/(9-cot(x))) ?
The first derivative of (8x/(9-cot(x))) is (8(9-cot(x)-xcsc^2(x)))/((9-cot(x))^2)