## anonymous 5 years ago Find the derivative of the function using the product rule (x)(sqrt(x^2+5))

1. anonymous

u'v+uv'

2. anonymous

you'll need the chain rule for the sqrt(x^2+5) term as well

3. anonymous

$\sqrt{{x ^2}+5}+x ^{2}/\sqrt{x ^{2}+5}$

4. anonymous

yep that looks right

5. anonymous

i got that but can i simplify it anymore?

6. anonymous

yeah you can multiply top and bottom by sqrt(x^2+5)

7. anonymous

the first term I mean

8. anonymous

(2x^2+5)/(sqrt(x^2+5))

9. anonymous

i mean i have to substitute my x in for the equation of the tangent line is it a good idea to just leave that like that?

10. anonymous

less computation if you simplify it a little further

11. anonymous

$x ^{2}/\sqrt{x ^{2}+5}$so i added it and got

12. anonymous

sorry 2x^2 +5 for numerator

13. anonymous

sorry 2x^2 +5 for numerator