What is the derivative of (5x/(6-cot(x))) ?

The derivative of (5x/(6-cot(x))) is (5(6-cot(x)-xcsc^2(x)))/((6-cot(x))^2)

What is the first derivative of (5x/(6-cot(x))) ?

The first derivative of (5x/(6-cot(x))) is (5(6-cot(x)-xcsc^2(x)))/((6-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{5 x}{6 - cot ( x )})

\frac{5 ( 6 - cot ( x ) - x csc ^{2} ( x ) )}{( 6 - cot ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x}{6 - cot ( x )})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{x}{6 - cot ( x )})

Apply the Quotient Rule:

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

= 5 \cdot \frac{\frac{d x}{d x} ( 6 - cot ( x ) ) - \frac{d}{d x} ( 6 - cot ( x ) ) x}{( 6 - cot ( x ) ) ^{2}}

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

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

= 5 \cdot \frac{1 \cdot ( 6 - cot ( x ) ) - csc ^{2} ( x ) x}{( 6 - cot ( x ) ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( 6 - cot ( x ) ) - csc ^{2} ( x ) x}{( 6 - cot ( x ) ) ^{2}} : \frac{5 ( 6 - cot ( x ) - x csc ^{2} ( x ) )}{( 6 - cot ( x ) ) ^{2}}

= \frac{5 ( 6 - cot ( x ) - x csc ^{2} ( x ) )}{( 6 - cot ( x ) ) ^{2}}

\int_{1}^{4} π (x - 1) d x

2 (2 - 3 x)^{2}

- 8 (x - 3)^{3} + 27

\int_{0}^{1} x^{k} d x

\int \frac{x ^{3}}{( x + 3 ) ^{4}} d x

What is the derivative of (5x/(6-cot(x))) ?
The derivative of (5x/(6-cot(x))) is (5(6-cot(x)-xcsc^2(x)))/((6-cot(x))^2)
What is the first derivative of (5x/(6-cot(x))) ?
The first derivative of (5x/(6-cot(x))) is (5(6-cot(x)-xcsc^2(x)))/((6-cot(x))^2)