# Thread: differentiation from first principles

1. ## differentiation from first principles

I understand the first section of this question but i can't get to the end.

it is differentiate from from first principles x+1/1-x

Thanks

2. Originally Posted by james863
I understand the first section of this question but i can't get to the end.

it is differentiate from from first principles x+1/1-x

Thanks
$f(x+h) - f(x) = \frac{1+x+h}{1-x-h} - \frac{1+x}{1-x}$

$\frac{1+x+h}{1-x-h} - \frac{1+x}{1-x} = \frac{(1+x+h)(1-x) - (1+x)(1-x-h)}{(1-x-h)(1-x)}$

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

This means,

$\lim_{h \to 0}\frac{f(x+h) - f(x)}{h} = \lim_{h \to 0}\frac{2}{(1-x-h)(1-x)} = \frac{2}{(1-x)^2}$