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Math Help - hyperbolic functions!!

  1. #1
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    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
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  2. #2
    Super Member wingless's Avatar
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    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)
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  3. #3
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    Quote Originally Posted by wingless View Post
    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
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