Question

How to derivate logarithmic and exponenetial functions ........?

Answer 1

show an example

Answer 2

ln(x) = 1/x is that what you are looking for?

Answer 3

I mean the derivative of ln(x) is 1/x or if it were 5ln(x) would be 5/x know what I mean?

Answer 4

\[\color{red}{\frac{d}{dx}e^x=e^x.}\]\[\color{blue}{\frac{d}{dx}a^x=a^x \log_e{a}.} \]\[\color{green}{\frac{d}{dx}\log_e{x}=\frac{1}{x}. }\]

Answer 5

Yes of coarse but please discuss more deeply that I understand clearly........... @mathdood

Answer 6

Okay do you want a proof of d/dx ln(x) = 1/x ?

Answer 7

Yes I want proof...... and I will a problem after a short while please solve it as well....

Answer 8

@mathdood

Answer 9

Okay I will try to do the proof just give me a second. This is one of those things you really just memorize though like d/dx sin(x) = cos(x) know what I mean? Anyway I will give it a shot.

Answer 10

Okay I am using the definition of a derivative to do this you are familiar with that right?

Answer 11

(x-2)/
ln(x+2) derivate...

Answer 12

Wait are you asking me to take the derivative of what you just typed or do you want the proof of ln(x) = 1/x ?

Answer 13

sorry d/dx ln(x) = 1/x I mean

Answer 14

Is this what you just type (x-2)/ln(x+2) ? If it is I just do this (x-2)*(ln(x+2))^-1 then use product rule. So (1/(ln(x+2))) + ((-1)(x-2)(1/(x+2))(1/(ln(x+2))^2)).

Answer 15

Now are you interested in the proof or?