## Ravus 3 years ago derivative of: sqrt(x) - x using the first principal. Please show work. The answer should be 1/[2*sqrt(x)]-1 I cant get the minus 1!

• This Question is Open
1. experimentX

i guess you know how to find the derivate of x ... so just find for sqrt(x)

2. Ravus

f(x) = $\sqrt{x} -x$

3. Ravus

oh...so just do them one at a time?:| That actually makes a lot of sense. the problem is I have the equation in the "definition of the derivative formula" and its not simplifying down right.

4. Ravus

where you take the limit as h-->0

5. experimentX

lim dx->0 (sqrt(x+dx) - sqrt(x))/dx now sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x) using binomial expansion, and removing higher terms --- close to linear expression we have: sqrt(x)(1+1/2*dx/x) or, lim dx->0 (sqrt(x)(1+1/2*dx/x) - sqrt(x))/dx or, lim dx->0 (1/2*dx/sqrt(x))/dx = 1/(2sqrt(x)) hence proved

6. lgbasallote

seems he wants the increment thingy...the limits

7. dpaInc

@Ravus , are you asking to take the derivative using the definition? (limit definition of derivative)

8. perl

@experimentX how do you get this sqrt(x+dx) = sqrt(x)*sqrt(1+dx/x)

9. dpaInc

@perl, nice avatar!

10. perl

hehe

11. Ravus

yes I want the "increment thingy"<<<thats exactally it! and yes dpalnc, I think it is the limit definition I mean.

12. experimentX

@perl .. take x common!

13. perl

huh?

14. dpaInc

|dw:1333351654824:dw| plug it in to that...

15. perl

(x+dx)^1/2 = x^1/2 + ...

16. perl

ohhhh

17. Ravus

yeah I did plug it in, and I get the right answer almost. I get 1/2*sqrt(x) but that whole thing should have a "-1"! i dont get that bit

18. perl

@experimentX (x+dx)^1/2 = x^1/2 ( 1 + dx/x ) ^1/2

19. experimentX

dx is supposed to be del x ... or better h

20. dpaInc

|dw:1333351804706:dw| do some algebra here....

21. dpaInc

ok... too many cooks... i'll quit.

22. Ravus

yeah I know what the formula is, but the algebra is giving me trouble

23. perl

@experimentX Very clever argument, so you looked at the binomial series and took the first two terms (linear )

24. experimentX

yes .. since dx^higer would be very less ... it would seem better to take linear term.

25. perl

then you factored out sqrt x

26. experimentX

yes .. and that would cancel out .. sqrt(x) leaving dx/(2sqrt(x)

27. Ravus

omg wow finally got it. simple algebra really. lmfao............

28. experimentX

congrats

29. gurvinder

|dw:1333354174909:dw|