# derivatives

• Apr 23rd 2010, 02:37 PM
steezin
derivatives
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.
• Apr 23rd 2010, 02:47 PM
skeeter
Quote:

Originally Posted by steezin
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 $\displaystyle h \to 0$
• Apr 23rd 2010, 02:54 PM
steezin
Thank you so much, turns out I mixed up one of the signs lol