calculating derivative with definiton

[Dorian Gray]

Greetings Mathematicians,


I am having difficulties with a problem. I need to find the derivative of a function f(x)= 1/[square root of (x-1)]

I need to use the defintion of [f(a+h) - f(a)] / h


I need to find f'(a). I canNOT use any formulas for this (only the definition. I worked the problem out to a certain point, but I do not know if it is correct OR if I should even addressing it this way.

Any advice, comments, suggestions, or tips are always greatly appreciated.View attachment 1681


Thanks again,
D

 

[Dorian Gray]

 

[galactus]

\(\displaystyle \frac{\frac{1}{\sqrt{x+h-1}}-\frac{1}{\sqrt{x-1}}}{h}\)

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

Multiply top and bottom by \(\displaystyle \sqrt{x-1}+\sqrt{x+h-1}\) and simplify using algebra.

After simplifying, the h in the top and bottom should cancel. Then, let the h's inside the radicals tend to 0 and you should get the derivative.

 

[Dorian Gray]

thank you

Thank you Galactus. Your suggestion was certainly appreciated.