Lambert W Function (domain, range, approximation, solving equations, derivative & integral)

Comparing the natural log function ln(x) and the product log function W(x).
0:00 ln(x) vs. W(x)
1. Solve e^x=2 & ln(2), 0:16
2. Solve xe^x=2 & W(2), 3:01
Newton's Method: https://youtu.be/EjUp_5X6io4
3. Domain, range, & graph for ln(x), 6:53
4. Domain, range, & graph for W(x), 9:16
5. Nice values for ln(x), 13:30
6. Nice values for W(x), 15:47
7. Solve e^x-e^(-x)=1, 19:54
8. Solve x+e^x=2, 22:40
9. Solve x^x=2, 25:25 (the t-shirt https://teespring.com/cute-math-cat-6)
10. Derivative of ln(x) by implicit differentiation, 27:30
11. Derivative of W(x) by implicit differentiation, 28:35
Integral of an inverse function, 32:50
12. Integral of ln(x) by the formula, 36:52
13. Integral of W(x) by the formula, 38:42
14. What's ln(i)? 43:50
15. What's W(-pi/2)? 46:11
Read more about the Lambert W function on Wikipedia: https://en.wikipedia.org/wiki/Lambert_W_function

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