## shahzadjalbani 3 years ago How to derivate logarithmic and exponenetial functions ........?

1. mathdood

show an example

2. mathdood

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

3. mathdood

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

4. maheshmeghwal9

$\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}. }$

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

6. mathdood

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

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

@mathdood

9. mathdood

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.

10. mathdood

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

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

12. mathdood

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 ?

13. mathdood

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

14. mathdood

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)).

15. mathdood

Now are you interested in the proof or?