Derivatives (12 videos)
Inverse Functions f ^1 (y) and the Logarithm x = ln y
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For the usual y = f(x), the input is x and the output is y.
For the INVERSE function x = f^1(y), the input is y and the output is x.
If y equals x cubed, then x is the cube root of y : that is the inverse.
If y is the great function e^x, then x is the NATURAL LOGARITHM ln y.
Start at y, go to x = ln y, then back to y = e^(ln y).
So the LOGARITHM is the EXPONENT that produces y.
The logarithm of y = e^5 is ln y = 5. Logarithms grow very slowly…….
Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.
Subtitles are provided through the generous assistance of Jimmy Ren.
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As Taught In:  Spring 2010 
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Undergraduate
