Question

use the first principle differential to find the derivative of y=Inx.

Answer 1

know the formula for 1st principle differential ?

Answer 2

yes

Answer 3

y=f(x) = ln x
so, can you find f(x+h)=..?

Answer 4

pls can u summarize the answer

Answer 5

i can help you to find it,
did you try this ?
if you are stuck at a step, tell me at which step.

Answer 6

well i stop at dy= In(x + dx)-In x

Answer 7

which formula are you using??
i might be using the other formula....

Answer 8

isn't it,
lim dx->0 (ln (x+dx)-ln x)/dx ?

Answer 9

yes it is

Answer 10

do you know (can you use) L'hopital's rule ?

Answer 11

no i dont know it, pls help

Answer 12

ok, then do you the formula for,
\(\large \lim \limits_{x \rightarrow 0} \ln (1+x)^{\dfrac{1}{x}}=...?\)

Answer 13

or,
\(\large \lim \limits_{x \rightarrow 0} {\dfrac{\ln (1+x)}{x}}=...?\)

Answer 14

^thats a standard limit that we can use here.

Answer 15

appreciate

Answer 16

but i was asking the value :P
anyways, its
\(\large \lim \limits_{x \rightarrow 0} {\dfrac{\ln (1+x)}{x}}=1\)

Answer 17

for your question,
you have \(\large \lim \limits_{dx \rightarrow 0} {\dfrac{ (\ln (x+dx)-\ln x)}{dx}} \\ \large =\lim \limits_{dx \rightarrow 0} {\dfrac{ \ln ((x+dx)/x)}{dx}}\\ \large =\lim \limits_{dx \rightarrow 0} {\dfrac{ \ln (1+dx/x)}{x(dx/x)}}=\dfrac{1}{x}\lim \limits_{dx \rightarrow 0} {\dfrac{ \ln (1+dx/x)}{(dx/x)}}\)
got this ?

Answer 18

yes, thanks

Answer 19

the limit on right =1 using that standard formula, so you are left with dy/dx = 1/x
which is your final answer for derivative of y-ln x
and welcome ^_^