Question

find f'(x) f(x)=sqrt X using f(x+h)-f(x) / h

Answer 1

conjugates is the key

Answer 2

\[\frac{f(x+h)-f(x)}{h}*\frac{f(x+h)+f(x)}{f(x+h)+f(x)}\]
\[\frac{(x+h)-(x)}{h(f(x+h)+f(x))}\]
\[\frac{h}{h(f(x+h)+f(x))}\]
\[\frac{1}{f(x+h)+f(x)}\]

Answer 3

and when h=0 by the limit we get:
\[\frac{1}{2f(x)}\]

Answer 4

the only reason that works for the top like that is cause f(x) = sqrt(x), its not that nice when its other things tho

Answer 5

ah i see

Answer 6

thanks

Answer 7

youre welcome