Second Derivative of Exponential Function

[Asphyxiated]

Homework Statement

Find the second derivative of:

$$e^{ax}$$

and

$$e^{-ax}$$

Homework Equations

The Attempt at a Solution

The book that I am using seems to have been very vague on how to take the derivatives of exponential functions. I am aware that:

$$\frac {d(e^{x})} {dx} = e^{x}$$

but it says literally nothing about how the chain rule applies to exponential function, or does it? Am I just making it too difficult? Please help!

 

[Mark44]

$$\frac {d(e^{u})} {dx} = e^{u} \frac{du}{dx}$$

 

[Gunthi]

Assuming "a" as a constant, you can consider two functions.

One is $$f(y)=e^y$$ and the other $$y=ax$$, so the derivative in respect to x would be:

$$\frac{df}{dx}=\frac{df}{dy}\frac{dy}{dx}=...$$.

You just need to calculate the differentials tand to the same again to get the result.

 

[Asphyxiated]

Ok so I tried the method listed, I am hoping someone can confirm that this is correct:

$$y = e^{ax}$$

$$y' = a(e^{ax})$$

$$y'' = a^2(e^{ax})$$

Thanks!

 

[Gunthi]

That's it ;)