Question

differentiate using the definition

Answer 1

\[\frac{ 1 }{ \sqrt{x} }\]

Answer 2

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

Answer 3

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

Answer 4

Do some algebra, cancel out the hs

Answer 5

\[\frac{ \frac{ 1 }{ \sqrt{x+h} }-\frac{ 1 }{ \sqrt{x} } }{ h }\]

Answer 6

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

Answer 7

\[\frac{ \frac{ \sqrt{x}+\sqrt{x-h}}{ \sqrt{x}\sqrt{x+h} } }{ h }\]

Answer 8

Typo up there ^

Answer 9

oops meant to put the h on the bottom :}

Answer 10

it's supposed to be a minus

Answer 11

all the way on top in the middle

Answer 12

oh ya that to

Answer 13

and the other one on top must be a plus

Answer 14

Inside the radical, too.

Answer 15

u mixed up the signs

Answer 16

oops!

Answer 17

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

Answer 18

twiddla time then.. hang on a sec

Answer 19

\[\frac{ -h }{ h \sqrt{x}\sqrt{x+h(\sqrt{x}+\sqrt{x+h})} }\]

Answer 20

h goes away

Answer 21

that square root is mess up in the bottom

Answer 22

yup

Answer 23

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

Answer 24

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

Answer 25

at what point do i make h = 0?

Answer 26

when u dont run into trouble if u do.

Answer 27

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