how to factor the derivative of f(x) = x^{5}(x + 6)^{6}?

I found the derivative to be f '= 5x^4(x+6)^6 + 6x^5(x+6)^5

if i set it equal to zero how would I find the x intercepts?

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  • Ed
    Lv 6
    1 decade ago
    Favorite Answer

    y = x^{5}(x + 6)^{6}

    use the product rule = Vdu/dx + Udv/dx

    u = x^5 v= (x+6)^6

    dy/dx = (x+6)^6 * (5x^4) + [x^5 * 6(x+6)^5]

  • 1 decade ago

    your in luck, that's what I just learned in math. OK, first change f(x) to y, it's the same thing. Write (x+6)six times, then multiply them all together, u know how to do F.O.I.L. right?(first, outer, inner, last- that's the order to multiply it in) After you get the answer, multiply the answer by x to the fifth power, then factor the answer to find the x's. If u have any questions u can email me.

  • Anonymous
    1 decade ago

    f '= 5x^4(x+6)^6 + 6x^5(x+6)^5

    f '= 5x^4(x+6)^6(6) + 6x^5(x+6)^5(6)

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