I need to find the derivative of y = sqrt(x-1), using the derivative formula f(x + h) - f(x) / h
At the moment I have sqrt((x+h) -1) - sqrt(x-1) / h
I tried multiplying the top and bottom by the conjugate but it didn't work.
it didn't? ...
$\displaystyle \frac{\sqrt{x+h-1} - \sqrt{x-1}}{h} \cdot \frac{\sqrt{x+h-1} + \sqrt{x-1}}{\sqrt{x+h-1} + \sqrt{x-1}}$
$\displaystyle \frac{(x+h-1) - (x-1)}{h(\sqrt{x+h-1} + \sqrt{x-1})}$
$\displaystyle \frac{h}{h(\sqrt{x+h-1} + \sqrt{x-1})}$
$\displaystyle \frac{1}{\sqrt{x+h-1} + \sqrt{x-1}}$
now take the limit as $\displaystyle h \to 0$