Question

f(x)= 1/x

simplify:

f(a+h) - f(a)
___________
h

I got h/a(a+h)
but I'm not sure if I am right.
please help if you can :)

Answer 1

f(a+h) = 1/(a+h)
f(a) = 1/a

so the difference quotient in your problem is: 1/h * (1/(a+h) - 1/a)

get common denominators there..i don't think you'll end up with an h at the top as per your answer.

Answer 2

\[\large \frac{\frac{1}{a+ h} + \frac{1}{a}}{h}\] lol im just latexing

Answer 3

f(a+h) = 1/(a+h)

f(h) = 1/a


so, what you ask for is:

\[\large \frac {\frac1{a+h} -\frac{1}{a}} {h}\]

Answer 4

Yes that @apoorvk

Answer 5

I did that and found the common denominators but I'm not sure if I got the right answer.

Answer 6

but my professor wants us to simplify that even more by finding the common denominators and going even further into it..

so tedious -.-

Answer 7

latex people....^^^

Answer 8

lol it seems i accidentally posted an answer :S against my principles psh psh

Answer 9

Did you do this? actually you should get:
\[\frac 1 {a(a+h)}\]


@dpaInc check your solution once - i seem to find an error.

Answer 10

well what was the common denominator?

I used ah(a+h)

Answer 11

i didn't post a solution...

Answer 12

just what sheep needed to simplify...

Answer 13

she...

Answer 14

how are you getting an 'ah(a+h)' in the denominator? you should get only a(a+h) - infact you should also get a 'negative' sign which I forgot to include.

Answer 15

@dpaInc I mean there seems to be a sign error - seems like you copied down the question incorrectly

Answer 16

i'm pretty sure what i wrote as the the difference quotient is correct... it's iggy that had a sign error... (sorry iggy.)

Answer 17

\[\large \frac {\frac1{a+h} -\frac{1}{a}} {h}\]
\[\large \frac {\frac{a-(a +h)}{a(a+h)}} h\]

Answer 18

I hate chrome!!! When I almost finished typing, snaps happened...
\[\frac{f(a+h) - f(a)}{h} = \frac{\frac{1}{(a+h)} - \frac{1}{(a)}}{h} = \frac{\frac{a}{a(a+h)} - \frac{(a+h)}{(a(a+h))}}{h}\]\[= \frac{\frac{a-a-h}{a(a+h)} }{h} = \frac{-h}{ah(a+h)} = -\frac{1}{a(a+h)} \]
It looks like differentiate an expression using the first principle :|

Answer 19

everything is being trumped now.... ^^^

Answer 20

huh?!

Answer 21

Thank you all for the help!

Answer 22

@Callisto switch to Firefox for OS.