The first example was y = x^x. It is a mix of the power function and the exponential function, but it's derivative is found by using logarithms. This idea of logarithmic differentiation is often used to find derivatives of "complicated" functions.
The other thing from class today was to emphasize that finding antiderivatives is a challenging exercise. One of the biggest mistakes I've seen students make in the past is using "bad" math - poor algebra skills typically. It gets easier with practice, but it does take some mental discipline.
Notes from today are posted below.
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