# Thread: prove the following formulas.......?

1. ## 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..??

2. ## Re: prove the following formulas.......?

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.