# [HELP] Derivative Of The Exponential !

1. Jan 8, 2010

### MiniSmSm

hi guys

I need The proof from definition of the derivative for exponential and log Fn
can somebody help me !!

2. Jan 8, 2010

### tiny-tim

Welcome to PF!

Hi MiniSmSm! Welcome to PF!

First, what definition of the exponential function are you using?

3. Jan 8, 2010

### MiniSmSm

Welcome Tiny-tim

I use e^x or a^x

4. Jan 8, 2010

### tiny-tim

Hi MiniSmSm!

(try using the X2 tag just above the Reply box )

Yes, but how are you defining ex ?

5. Jan 8, 2010

### MiniSmSm

I don understand !
I mean as a power series

6. Jan 8, 2010

### tiny-tim

You mean ∑0 xn/n! ?

ok, then just differentiate that …

what do you get?

7. Jan 8, 2010

### MiniSmSm

No no ..

I mean by using this formula

F(x+h)-F(x) / h ( sorry I dont know how to use tags :( )

how can I prove that the derivative of that function equals to its own !

8. Jan 8, 2010

9. Jan 8, 2010

### MiniSmSm

thank you
this is what I wanted

10. Jan 9, 2010

### HallsofIvy

Staff Emeritus
That proof requires the fact that $e^{x+y}= e^xe^y$. Have you proved that from the power series definition? If so, how?

11. Jan 10, 2010

### MiniSmSm

Actually I havent :(
how ?