# Differentiation of an exponential function

1. Jul 17, 2006

### pavadrin

Hey,
I have a problem involving natural logs which has got me confused, even though it appears simple.
The problem: Find the exact coordinates of the point on $$y = e^x$$ where the gradient is 2.
From previous experience, I know that differentiation is required, but because of the e I am not sure on how to go about this. After the differentiation I think I can manage to complete it.
Thanks,
Pavdarin

2. Jul 17, 2006

### d_leet

Well what is the derivative of $$y = e^x$$?

3. Jul 17, 2006

### sdekivit

if you don't know it you can find out using the given that d/dx ln x = 1/x and then calculate d/dx ln $$e^x$$ using the chain rule

4. Jul 17, 2006

### Benny

If you know how to do this kind of problem then all you need is the derivative of e^x which is just e^x. Just do this problem as you would do if "y" was any other function, for example a polynomial.

5. Jul 17, 2006

### pavadrin

thanks for the help, however i am still unsure on how to approach this problem

6. Jul 17, 2006

### sdekivit

the derivative is the gradient, so the following must be solved:

$$\frac {dy} {dx}\ = 2$$

This will give you the x-coordinate.

Last edited: Jul 17, 2006
7. Jul 17, 2006

### HallsofIvy

You "approach" this problem by differentiating ex! What is the derivative of ex? (It's the world's easiest derivative!)

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