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Find the outside and inside functions of the following to find their derivatives:

1) sqrt(2x+9)

2) cos(cos(x))

3) tan(x)

I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.

  • Calculus -

    The chain rule says that if we have u(x) and f(u(x)),

    df/dx = df/du * du/dx

    f is the outside function, u is the inside.

    So, in the first case
    f(u) = √u
    u(x) = 2x+9

    f(u) = cos(u)
    u(x) = cos(x)

    #3. Is almost a trick question.
    f(u) = tan(u)
    u(x) = x

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