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Differentiate with respect to x (3x^2-5ax+a^2)^4

  • calculus - ,

    This is a typical problem using the chain rule: if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx

    Here, let u = 3x^2 - 5ax + a^2
    So, y = u^4
    dy/du = 4u^3
    du/dx = 6x - 5a

    dy/dx = 4u^3 * (6x-5a)
    = 4(3x^2 - 5ax + a^2)^3 * (6x-5a)

    Don't let the a's bother you. They're just some number, like 3 or -4, just one we don't happen to know. Just carry them through like any other constant.

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