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..??

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.