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

The derivative of 1/x+1/(1-x) is (2x-1)/(x^2(-x+1)^2)

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{x} + \frac{1}{1 - x}

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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

a re a 2 x^{2}, 2 x + 6, 0, 1

\int x (x - a)^{3} d x

\int ln ∣ (x) ∣ d x

\int 2 tan (x) sec (x) d x

s l o p e in t erce pt (16, 13), (- 8, - 17)

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