# Math Help - hyperbolic functions!!

1. ## hyperbolic functions!!

Find the derivative of the function g(t) = cosh^3(t).

ok, so i know the correct answer for this one:

3cosh^2(t)sinh(t)

now i would like someone to show me how exactly to get that answer...
thanks

mathlete

2. Let $h(t) = \cosh^3 t$

We can write it as,
$f(g(t))$ where $f(t) = t^3$ and $g(t) = \cosh t$.

Simply use the chain rule.

Chain rule:
$[f(g(t))]' = f'(g(t))\cdot g'(t)$

3. Originally Posted by wingless
Let $h(t) = \cosh^3 t$

We can write it as,
$f(g(t))$ where $f(t) = t^3$ and $g(t) = \cosh t$.

Simply use the chain rule.

Chain rule:
$[f(g(t))]' = f'(g(t))\cdot g'(t)$
oh ok, so the derivative of cosh(t) is just sinh(t), thats what i was having trouble with, but i guess its easier than i was making it...
thanks