## anonymous 5 years ago how do i find the derivative of this using the chain rule please help somebody$F(x)=x \sqrt{x ^{2}+1}$

1. bahrom7893

Okay first throw the x into the sqrt.

2. bahrom7893

F(x) = sqrt(x^4 + x^2)

3. bahrom7893

Or F(x) = (x^4+x^2)^(1/2)

4. bahrom7893

Now take the derivative: F'(x) = (1/2) * (x^4 + x^2 )^(-1/2) * (4x^3 + 2x)

5. bahrom7893

$f'(x) = (4x^3+2x)/(2\sqrt(x^4+x^2))$

6. anonymous

can u please explain the part when u threw the x into the square root

7. bahrom7893

okay x is the same as $\sqrt{x^2}$

8. anonymous

yep

9. bahrom7893

so to put it inside the sqrt, multiply everything inside by x^2

10. anonymous

ok great thank u soo much appreciate the help :)

11. bahrom7893

Can you click on Become a fan next to my name, please! Thanks =)

12. anonymous

sure

13. anonymous

can i ask u another question lol ?