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

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

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

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

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derivative of

f (x) = \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}}

\int \frac{x ^{3}}{( 5 x + 2 ) ^{3}} d x

\int \frac{e ^{x}}{e ^{x} + 3} d x

\int sin (3 x) sin (4 x) d x

\int (x^{3} + 3)^{\frac{1}{4}} x^{5} d x

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