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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral from-3 to 3 of (27/2-3/2 x^2)

\int_{- 3}^{3} (\frac{27}{2} - \frac{3}{2} x^{2}) d x

limit as x approaches 0-of (x-2)/(x^2-4)

x \to 0 - lim (\frac{x - 2}{x ^{2} - 4})

derivative of ((qx+r))/((sx+t))derivative of

\frac{( q x + r )}{( s x + t )}

f(x)=(e^x)/(3x^2+2x^4)

f (x) = \frac{e ^{x}}{3 x ^{2} + 2 x ^{4}}

derivative of 2x(7x^2-2^4)

\frac{d}{d x} (2 x (7 x^{2} - 2)^{4})

Frequently Asked Questions (FAQ)

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