# prove the following formulas.......?

• Jul 6th 2011, 06:39 PM
Yukina
prove the following formulas.......?
prove the following formulas.......?

1) If f(x)= (x+1)sqrt(x^2-2x+2) then f'(x)=(2x^2-2x+1)/sqrt(x^2-2x+2)

2) If f(x)= sin(2x)/ [1+cos(2x)] then f'(x)= 2/[1+cos(2x)]

3) If f(x)= cos^2sqrt(x) then f'(x)= -sin[2sqrt(x)]/2sqrt(x)

I have no idea to solve these problems.....
Can anyone help me, please..??

• Jul 6th 2011, 06:52 PM
Sudharaka
Re: prove the following formulas.......?
Quote:

Originally Posted by Yukina
prove the following formulas.......?

1) If f(x)= (x+1)sqrt(x^2-2x+2) then f'(x)=(2x^2-2x+1)/sqrt(x^2-2x+2)

2) If f(x)= sin(2x)/ [1+cos(2x)] then f'(x)= 2/[1+cos(2x)]

3) If f(x)= cos^2sqrt(x) then f'(x)= -sin[2sqrt(x)]/2sqrt(x)

I have no idea to solve these problems.....
Can anyone help me, please..??

Hi Yukina,

For the first and second use the Product rule of differentiation with the Chain rule. For the third you have to only use the Chain rule. I hope you can give it a try now.