Help needed off the maths minds please

it's not sqrt (x+h) it's f(x+h) same with the x term

define f(x)=x^1/2

therefore f(x+h)= (x+h)^1/2

seperate the terms from the brackets and then sub into to your lim equation

your h term on the bottom will cancel out leaving you with just a simple equation with an h term in it, which as h=0 will go.

I would do the working for you, but have a go at it, I'll help if you get stuck :)

Maths minds on Betfair...you are having a laugh

aussi your approach is what I normally try however it doesn't really work for fractional powers cos you can't simplify the brackets.

done it..

multiplied the fraction by (sqrt(x + h) + sqrt(x)) to get h/[h(sqrt(x + h) + sqrt(x)] which leaves 1/(sqrt(x + h) + sqrt(x))... rest is trivial

It's the difference of two squares.

you can make your equation

((x+h)^1/2-(x^1/2))((x+h)^1/2+x^1/2)) all divided by h((x+h)^1/2+x^1/2)) perfectly ok to do that algebraicly as you are multiplying by 1.

simplified down that gets you to x+h-x/h((x+h)^1/2+x^1/2)

Cancelling the h gives 1/(x+h)^1/2+x^1/2

as h tends to zero we get

1/2(x^1/2)

dy/dx or f'(x) whichever you prefer = 1/2x^1/2

I hope that is clear, I hate doing these things in text, you should probably write that down slowly in proper notation, some of the brackets maybe amiss.

ah. I misunderstood your first post. I thought you were suggesting to mmultiply out (x+h)^1/2 uing binomial. I ended up doing it the same way as you. Thanks for your help, appreciated.