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About C30N9

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  1. Today, in my Calc II exam, I've came across the question of finding the derivative of an inverse function when x = 2. The function was as I remember:

    f(x) = e ^ 2x + 4x + 1

    I didn't know how to solve for x algebraically after I substituted f(x) with 2 (or using ln or exp functions). So I put automatically x = 0 as it will satisfy the equation and then I proceeded. Luckily, it was a multiple choice question, so the method of solving isn't important.

    How do I solve this?

    1. Show previous comments  4 more
    2. Ribbiks


      Somehow I doubt that's how they expected you to solve it. Unless they actually teach kids the Lambert W function in Calc II nowadays? There's probably some simpler trick I'm not aware of, been ages since I touched this stuff.

    3. C30N9


      That's correct, I got 1/6 during the exam.

      They do teach complex numbers in Calc II, just not before transcendental functions. I don't know if it includes Lambert W function though.

      It's not fair to include such question in this exam if this is the only solution.

    4. Fredrik


      You don't really need to know about the Lambert W function unless you're solving a more general version of the problem. Here you just need the inverse at one specific value, y = 2, and since it's an exam problem, this point was naturally chosen so that the input x = 0 can be found by just inspecting the equation.

      This is a typical feature of exam problems, less common in real world problems.