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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?
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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.
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.