find f'(a)

Question

f(x) = root(x-1)

so I did the lim h->0 f(x+h) - f(x) / h
but I don't know how to get the h out of the denominator

Answer 1

too bad you didn't show us your work
(f(x+h) - f(x))/h = (√(x-1+h) - √(x-1))/h
Now multiply top and bottom by the "conjugate"
(√(x-1+h) - √(x-1))*(√(x-1+h) + √(x-1)) / h(√(x-1+h) + √(x-1))
((x-1+h) - (x-1)) / h(√(x-1+h) + √(x-1))
h/h(√(x-1+h) + √(x-1))
1/(√(x-1+h) + √(x-1))
Now, as h→0, that is 1/(2√(x-1))