Find d/dx of hyperbolic function

[silicon_hobo]

[SOLVED] find d/dx of hyperbolic function

Homework Statement

Find:
http://www.mcp-server.com/~lush/shillmud/1.1A.Q.JPG

Homework Equations

d/dx f(x)*g(x) = f(x) * d/dx g(x) + g(x) * d/dx f(x)
d/dx f(g(x)) = d/dx f(g(x))* d/dx g(x)
d/dx sinh x = cosh x
d/dx cosh x = sinh x

The Attempt at a Solution

http://www.mcp-server.com/~lush/shillmud/1.1A.A.JPG

Can this be further simplified? When I run it in maple I get:
http://www.mcp-server.com/~lush/shillmud/1.1A.C.JPG

I'm probably going to be posting here often so let me give you a little background. I am beginning calc II by correspondence. It is the last course of my undergrad and I haven't done any pure math courses in a while. I think things are going alright so far but without a prof or fellow students I sometimes become stuck or find it difficult to check an answer in a way that allows me to move on to the next question with confidence. I thought maple might help me check my answers but in this case it's left me more confused. Thanks for reading!

P.S. How do I use special math characters (like infinite etc.) in my post as have seen some people do?

 

[HallsofIvy]

What you have is perfectly correct. I can't speak for the Maple (especially not if they include "ln(e)" in the answer!

 

[Hurkyl]

I expect it's simply a matter of applying a (hyperbolic) trig identity to show they are equal.

Plugging in 5 or 6 (non-special!) values of x should, at least, give you high confidence that those expressions are, in fact, equal.