What is the limit as h approaches 0 of (((1/(1-(x+h)))-(1/(1-x))))/h ?

The limit as h approaches 0 of (((1/(1-(x+h)))-(1/(1-x))))/h is 1/((-x+1)^2)

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limit as h approaches 0 of (((1/(1-(x+h)))-(1/(1-x))))/h

h \to 0 lim \frac{( ( \frac{1}{1 - ( x + h )} ) - ( \frac{1}{1 - x} ) )}{h}

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

Solution steps

h \to 0 lim (\frac{\frac{1}{1 - ( x + h )} - \frac{1}{1 - x}}{h})

Simplify

\frac{\frac{1}{1 - ( x + h )} - \frac{1}{1 - x}}{h} : \frac{1}{( - x + 1 ) ( - h + 1 - x )}

= h \to 0 lim (\frac{1}{( - x + 1 ) ( - h + 1 - x )})

Plug in the value

h = 0

= \frac{1}{( - x + 1 ) ( - 0 + 1 - x )}

(- x + 1) (- 0 + 1 - x) = (- x + 1)^{2}

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

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

x \to + 0 + lim ((1 + x)^{(\frac{1}{x})})

\frac{d y}{d x} = 1 + y - x

3 x^{2} - 6 x - 9, at x = 3

\frac{\partial}{\partial y} (\frac{x y ^{2}}{x ^{2} y ^{3} + 1})

What is the limit as h approaches 0 of (((1/(1-(x+h)))-(1/(1-x))))/h ?
The limit as h approaches 0 of (((1/(1-(x+h)))-(1/(1-x))))/h is 1/((-x+1)^2)