Derivatives (12 videos)

Six Functions, Six Rules, and Six Theorems

This lecture compresses all the others into one fast video for review of derivatives.

Five of the 6 functions are old, the new one is a STEP function.  Slope = DELTA function.
The 6 rules cover f + g, f times g, f divided by g, chains f(g(x)), inverse of f, and then L’HOPITAL for 0/0

The 6 theorems include the Fundamental Theorem of Calculus for INTEGRAL OF DERIVATIVE OF f(x) 
Function 1 is f(x)   Function 2 is its slope (rate of change)   Add up those changes to recover f(x)  !!

The MEAN VALUE THEOREM says that if your average speed is 70,  then instant speed is 70 at least once
The BINOMIAL THEOREM tells you the series that adds up to the pth power f(x) = (1 + x)^p

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here .

Subtitles are provided through the generous assistance of Jimmy Ren.

Transcript
Related Resources

Course Info