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Derivative of f(x) = cos pi*x

  1. Nov 7, 2005 #1
    How would I do the derivative of

    f(x) = cos pi*x

    I know f'(x) cos x = - sin x but what about that pi?
  2. jcsd
  3. Nov 7, 2005 #2
    Are you familiar with the chain rule ?
  4. Nov 7, 2005 #3

    James R

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    The chain rule is

    [tex]\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}[/tex]

    Take y = cos u

    then you know that dy/du = -sin u.

    Now put u = nx, for n a constant.

    You know that du/dx = n

    Now consider:

    y = cos nx

    Put u = nx, so that y = cos u. Then the chain rule tells us:

    [tex]\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}[/tex]
    [tex]= (-\sin u)(n)[/tex]
    [tex]= -n\sin nx[/tex]
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