## anonymous 3 years ago find the derivative of f(x)=sqrt (x^2+2x)

1. anonymous

$f(x)=\sqrt{x^2+2}$

2. anonymous

$$f(x)=(x^2+2)^{1 \over 2}$$

3. anonymous

thats not one of the choices

4. anonymous

noooooooo its easier to solve in this format

5. anonymous

huh

6. anonymous

#4

7. anonymous

$1\div2\sqrt{x ^{2}+2x}\times(2x+2)$

8. anonymous

$$f(x)=(x^2+2)^{1 \over 2}$$ is the same as $$f(x)= \sqrt{x^2+2}$$

9. zepdrix

Sandy, it's easier to differentiate a root if you rewrite it as a fractional exponent :) She was just rewriting the problem a little nicer for you, not the solution. :D

10. anonymous

i understand but the assignment is keeping it that way so im getting confused thats all

11. zepdrix

it might be a good idea to switch to a fractional exponent, do the differentiation, then as your last step, put whatever fractional exponent you have back into root form. UNLESS you remember the derivative of sqrt(x), then you skip doing that step ^^

12. zepdrix

swiss is typing up a storm :P she prolly got something for you lol

13. anonymous

lol

14. zepdrix

she might just be trolling us, it's hard to tell at this point -_- lol

15. anonymous

$$f(x)=(x^2+2)^{1 \over 2}$$ $${1 \over 2}(x^2+2)^{({1 \over 2}-1)}*2x$$ $${1 \over 2}(x^2+2)^{-1 \over 2}*2x$$ $$\large { 1 \over 2\sqrt{x^2+2}}*2x$$ $$\large {2x \over 2(x^2+2)}$$ $$\large {x \over (x^2+2)}$$

16. anonymous

okkk i had to post loil but if you are still interested I can explain what i did

17. zepdrix

Woops! Your sqrt disappeared on the last couple steps there! <:o

18. anonymous

@zepdrix was getting too curious

19. anonymous

uuugghhhhhhhhhh

20. zepdrix

XD

21. anonymous

i hate latex it never listens

22. anonymous

ok one more time at it

23. anonymous

:(

24. anonymous

ok thanks

25. anonymous

you guys rock

26. zepdrix

Do the first 3 steps make sense though sandy? c: those she did correctly.

27. anonymous

ok lets explain the first 3 steps that last 2 steps are basic simplification neways

28. anonymous

u used the power rule first

29. anonymous

I used the chain rule by first bringing down the exponent in front of the bracket and then subtracting one from the exponent as you can see and then I derived what was in the bracket. The derivative of x^2+2 is 2x

30. anonymous

Well as we see there are 2 things that need to be derived. The outer exponent and the inner exponent. So the chain rule states that you first derive the outer part and then you derive what is in the bracket

31. anonymous

32. anonymous

alrighty ill just give you the last two lines that i messed up $$\large {2x \over 2\sqrt{x^2+2}}$$ $$\large {x \over \sqrt{x^2+2}}$$

33. anonymous

i dont get what this means