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Popular >

derivative of (x+1/(x-1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of cos(x)

x \to 0 lim (cos (x))

integral of (sqrt(x^2-49))/(x^4)

\int \frac{x ^{2} - 49}{x ^{4}} d x

integral of 1/(x(1-x^2))

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

derivative of (60/(0.01x^2+1))

\frac{d}{d x} (\frac{60}{0.01 x ^{2} + 1})

derivative of-9/(sqrt(x))

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

Frequently Asked Questions (FAQ)

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