What is the derivative of (2x/(sqrt(2x-1))) ?

The derivative of (2x/(sqrt(2x-1))) is (2(x-1))/((2x-1)sqrt(2x-1))

What is the first derivative of (2x/(sqrt(2x-1))) ?

The first derivative of (2x/(sqrt(2x-1))) is (2(x-1))/((2x-1)sqrt(2x-1))

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}{2 x - 1})

\frac{2 ( x - 1 )}{( 2 x - 1 ) 2 x - 1}

Solution steps

\frac{d}{d x} (\frac{2 x}{2 x - 1})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 ( x - 1 )}{( 2 x - 1 ) 2 x - 1}

\int x^{5} e x^{6} + 1 d x

f (x) = - 5 x^{4}

\int (cos (2 x) e^{2 x}) d x

\int \frac{x + 2}{( x ^{2} + 2 x + 10 ) ^{\frac{5}{2}}} d x

f (x) = 5 x^{4}

What is the derivative of (2x/(sqrt(2x-1))) ?
The derivative of (2x/(sqrt(2x-1))) is (2(x-1))/((2x-1)sqrt(2x-1))
What is the first derivative of (2x/(sqrt(2x-1))) ?
The first derivative of (2x/(sqrt(2x-1))) is (2(x-1))/((2x-1)sqrt(2x-1))