## sandy524 Group Title find the derivative of f(x)=sqrt (x^2+2x) one year ago one year ago

1. sandy524 Group Title

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

2. swissgirl Group Title

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

3. sandy524 Group Title

thats not one of the choices

4. swissgirl Group Title

noooooooo its easier to solve in this format

5. sandy524 Group Title

huh

6. sandy524 Group Title

#4

7. rajdoshi Group Title

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

8. swissgirl Group Title

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

9. zepdrix Group Title

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. sandy524 Group Title

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

11. zepdrix Group Title

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 Group Title

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

13. sandy524 Group Title

lol

14. zepdrix Group Title

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

15. swissgirl Group Title

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

16. swissgirl Group Title

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

17. zepdrix Group Title

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

18. swissgirl Group Title

@zepdrix was getting too curious

19. swissgirl Group Title

uuugghhhhhhhhhh

20. zepdrix Group Title

XD

21. swissgirl Group Title

i hate latex it never listens

22. swissgirl Group Title

ok one more time at it

23. sandy524 Group Title

:(

24. sandy524 Group Title

ok thanks

25. sandy524 Group Title

you guys rock

26. zepdrix Group Title

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

27. swissgirl Group Title

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

28. sandy524 Group Title

u used the power rule first

29. swissgirl Group Title

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. swissgirl Group Title

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. swissgirl Group Title

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