# First and second derivatives

• May 16th 2013, 06:39 PM
Oldspice1212
First and second derivatives
Howdy, just a quick question,

y = 4x/(square root (x+1)

I have to find y' and y''

I have this as my y'

4(square root(x+1) - 2x/(square root x+1) all of this divided by x+1

I can show my work if you want but it's just tedious writing it out on this, I can show it though if you like. (If my y' is wrong that is)
My question is for y'' do I have to use product rule on the 4(square root x +1) then a quotient rule on 2x/( square root x+1) and then another quotient rule for the overall derivative? BLAH, I want to know if I'm over doing it or if it really is the right process.

Thank you as always.
• May 16th 2013, 08:00 PM
ibdutt
Re: First and second derivatives
• May 16th 2013, 08:20 PM
Oldspice1212
Re: First and second derivatives
How did you get Square root(x+10)?

Edit: ah mistake for a parenthesis

Shouldn't the denominator be just (x+1) since the square root gets cancelled out by 2​?
• May 16th 2013, 08:33 PM
ibdutt
Re: First and second derivatives
You are absolutely right it is a typing error. It is sqrt ( x+1)
• May 16th 2013, 08:44 PM
Oldspice1212
Re: First and second derivatives
I'm still a bit confused on why the deno. is (x+1)^3/2 since it's g(x)^2 = (root x+1)^2 cancel out the root = x+1

EDIT: I figured it out, I just had to do a bit more algebra, ty :)