Derivatives of $\sinh x$ and $\cosh x$ Can someone give me an intuitive explanation about the derivatives of $\sinh x$ and $\cosh x$? Something similar to:
Intuitive understanding of the derivatives of $\sin x$ and $\cos x$
Thanks!

There are the six hyperbolic functions and they are defined as follows.

Here are the graphs of the three main hyperbolic functions.
 

We also have the following facts about the hyperbolic functions.

You’ll note that these are similar, but not quite the same, to some of the more common trig identities so be careful to not confuse the identities here with those of the regular trig functions.

Because the hyperbolic functions are defined in terms of exponential functions finding their derivatives is fairly simple provided you’ve already knew.  We haven’t however so we’ll need the following formula.

With this formula we’ll do the derivative for hyperbolic functions.

For the rest we can either use the definition of the hyperbolic function and/or  the quotient rule.  Here are all six derivatives.
