## Calle87 3 years ago differentiate using the definition

1. Calle87

$\frac{ 1 }{ \sqrt{x} }$

2. bahrom7893

it's lim as h->0 (f(x+h)-f(x))/h

3. bahrom7893

f(x+h) = 1/sqrt(x+h) f(x) = 1/sqrt(x)

4. bahrom7893

Do some algebra, cancel out the hs

5. Calle87

$\frac{ \frac{ 1 }{ \sqrt{x+h} }-\frac{ 1 }{ \sqrt{x} } }{ h }$

6. bahrom7893

yea, now multiply by the conjugate i think.. both top and bottom

7. Calle87

$\frac{ \frac{ \sqrt{x}+\sqrt{x-h}}{ \sqrt{x}\sqrt{x+h} } }{ h }$

8. across

Typo up there ^

9. Calle87

oops meant to put the h on the bottom :}

10. bahrom7893

it's supposed to be a minus

11. bahrom7893

all the way on top in the middle

12. Calle87

oh ya that to

13. bahrom7893

and the other one on top must be a plus

14. across

15. bahrom7893

u mixed up the signs

16. Calle87

oops!

17. Calle87

ok so i got all that part, the conjugates are what get me

18. bahrom7893

twiddla time then.. hang on a sec

19. Calle87

$\frac{ -h }{ h \sqrt{x}\sqrt{x+h(\sqrt{x}+\sqrt{x+h})} }$

20. Calle87

h goes away

21. Calle87

that square root is mess up in the bottom

22. bahrom7893

yup

23. bahrom7893

No, since h is 0, on the bottom u just have sqrt(x+0)

24. bahrom7893

so it's -1/sqrt(x) which is correct

25. Calle87

at what point do i make h = 0?

26. bahrom7893

when u dont run into trouble if u do.

27. bahrom7893

1/h <- NO 1/(4+1) <- YES