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# C30N9

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1. ## C30N9

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. `code:Array`
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. 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. 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.

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