calculus

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What does it mean to be be an inside or outside function?
for example:
tell which is the inside function and which is the outside:
f(x)=sin3x

  • calculus -

    The idea is that
    df (g(x) )/dx = df/dg * dg/dx
    where f is the "outside function and g is the "inside" function
    You do the outside function derivative first, then the inside function
    so for your example we have
    f ( g(x) ) = sin (g(x)) = sin ( 3x )
    f (g) = sin g outside
    g = 3x inside
    so in your case
    df/dg = cos g outside = cos 3x
    dg/dx = 3 inside
    so df/dx = cos g * 3
    or 3 cos 3x

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