Discovering the Derivate Definition for f(x) = x/(2x-1)

[ladyrae]

Thanks for your help...

How about this one?

Using the definition of derivate find f ` (x)

f(x) = x/(2x-1)

f ` (x) = lim h->0 [(f(x+h)) – (f(x))]/h

lim h->0 ([((x+h) / (2x+2h-1))-(x/(2x-1))]/h) . [((2x+2h-1)(2x-1)) / ((2x+2h-1)(2x-1))]

lim h->0 [(2x^2)-x+(2xh)-h-(2x^2)-(2hx)+x]/(h(2x+2h-1)(2x-1))

lim h->0 -h/(h(2x+2h-1)(2x-1)) = -1/(2x-1)^2

 

[arildno]

If f(x)=x/(2x-1), then it is correct.

 

[ladyrae]

typo

yes...thanks

 

[arildno]

just a suggestion, ladyrae:
if you have more questions on this, don't open any new thread, continue to use this instead.
In addition, try to learn LATEX formatting, it's not very difficult..