# Differentiating Hyperbolic Functions

1. Apr 17, 2010

### BoT

1. Differentiate cosh(x) using first principles

2. cosh(x) = (e^x+e^-x)/2

From previous exercises, I know the answer will be sinh(x)= (e^x-e^-x)/2 but I cannot get to the answer.
I seem to be left with the equation: lim h ---> 0 (e^2x*e^2h +1-e^h*2e^x +e^h)/(2h*e^x*e^h)
But when you make h=0 , it becomes underfined???
1. The problem statement, all variables and given/known data

2. Apr 17, 2010

### rock.freak667

Where did you get e2x and whatnot from?

Just simplify

$$\frac{e^{x+h}+e^{-(x+h)}-(e^x+e^{-x})}{2h}$$

and then factorize.

3. Apr 17, 2010

### BoT

I got it to

ex*eh+e-x*e-h -ex -e-x/ 2h

But how do I simplify this?
This is the part that always screws me up!

4. Apr 17, 2010

### rock.freak667

Factor out ex from ex*eh and ex. Do a similar exercise with e-x from the terms.

Then compute the limits.