Math SOmeone please please help

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Find the derivative of the function.
g(u) = (5+u^2)^5(3-9u^2)^8

Could someone please explain the steps that would lead me to the answer? I'm completely stuck.

  • Math differentiation+substitution -

    We can solve this by differentiation of a function of a function.

    Given
    g(u) = (5+u^2)^5(3-9u^2)^8
    let
    p(u)=(5+u²), and
    q(u)=(3-9u²)

    Then
    g(u)=p(u)^5 * q(u)^8
    Using the chain rule, we get
    d(p(u)^5)/du
    =5p(u)^4*dp(u)/du
    =5p(u)^4*2u ...(1)
    Similarly,
    d(q(u)^8)/du
    =8q(u)^7*d(q(u))/du
    =9q(u)^7*(-18u) ... (2)

    Now apply the product rule to the original function g(u):

    d(g(u))/du
    =(p(u)^5*d(q(u))/du + d(p(u))/du * q(u)^8

    Substitute (1) and (2) and simplify to get:
    13122*u*(u^2+5)^4*(3*u^2-1)^7*(39*u^2+115)
    or some equivalent expression.

  • Math SOmeone please please help -

    Go to : calc101 com

    Click option derivatives

    In rectacangle:Take the derivative of
    type:

    ((5+u^2)^5)((3-9u^2)^8)

    In rectacangle:with respect to:
    type u

    In rectacangle:and again with respect to
    type u

    Then click option: DO IT

    You will see solution step-by-step

    By the way on this site you can practice any kind of derivation.

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