How on Earth Do You Differentiate That?
<p>This is an infinite power tower of <em>x</em>. You may have seen such a tower equated to a number, which is then solved to give an unexpectedly clean solution. The natural next step is (of course) to take the derivative.</p>
<p>There are a few too many <em>x</em>s here to use the chain rule, to say the least. If the power tower was, say, 10 tall, this would be excruciating but possible. The infinite height makes this problem a lot easier — notice that at each point in the tower, we still have an infinite tower from that point onwards. We can simplify the problem with the following substitution:</p>
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