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Core 3 Differentiating Expo Help Pleaseee

Hi, my teacher went through this on Friday and I rushed to write it down. However I cant seem to work out what the hells going on.Could someone go through this for me so that hopefully I can see the correct way of doing things?Thanks

Find the equation of the tangent to the following graphs for the given values of x

y=ln ex

, where

x=1

Thanks

lnex?

Do you mean y=lne^x?

No, as in ln x
spoken verbally as 'log x'

Reply 4

Small123

moonaldo99

No, as in ln x
spoken verbally as 'log x'

ln(ex) \not= lnx

Reply 5

moonaldo99

sorry, I meant y=ln ex, or am I still not being clear enough?

Reply 6

heresjohno

then it's just 1/x if you are differentiating lnx?

Reply 7

Small123

moonaldo99

sorry, I meant y=ln ex, or am I still not being clear enough?

Do you mean

log_e x

ln(ex)

.
If its the former then the derivative of

lnx

\dfrac{1}{x}

and for a general function

f(x)

\dfrac{f'(x)}{f(x)}

Reply 8

Danielllll

to find the equation of the tangent, you need to know the gradient at that point. So you need to differentiate ln(x) and sub in your x value to find the gradient. can you go from there?

Reply 9

heresjohno

moonaldo99

sorry, I meant y=ln ex, or am I still not being clear enough?

or if you mean ln (e^x) then it's just y=x...

Reply 10

moonaldo99

Yes but there is also the added problem of finding the tangent to that line when x=1

Reply 11

moonaldo99

Danielllll

to find the equation of the tangent, you need to know the gradient at that point. So you need to differentiate ln(x) and sub in your x value to find the gradient. can you go from there?