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Sinusoidal functions

Differentiation. Derivatives and differentials. Products and quotients. Power rule. Chain rule. Sinusoidal functions. Slope and derivative. 0. Differentials are not numbers. +5. +4. +3. +2. +1. 0. -1. -2.

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Sinusoidal functions

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  1. Differentiation Derivatives and differentials Products and quotients Power rule Chain rule Sinusoidal functions

  2. Slope and derivative 0

  3. Differentials are not numbers +5 +4 +3 +2 +1 0 -1 -2 • Pairedappearances of df and dx, such as in , refer to the shrinkage of Dxwith the correspondingamount of shrinkage inDf. Think of differentials as shorthand instructions for limiting processes rather than as numbers. • When you find an equation with a differential df, can you find its partner? Can you draw a triangle having legs with lengths Df and Dx? • Regardless of how closely we look in this course, we find no tick marks on the number line corresponding to df or dx. Differentials are not numbers. -3 -4 -5 #

  4. Weierstrass function 0

  5. Differentiation Derivatives and differentials Products and quotients Power rule Chain rule Sinusoidal functions

  6. Derivative of a quadratic function 0

  7. Derivative of power law 0

  8. Derivative of power law 0

  9. Differentiation Derivatives and differentials Products and quotients Power rule Chain rule Sinusoidal functions

  10. Chain rule 0

  11. Differentiation Derivatives and differentials Products and quotients Power rule Chain rule Sinusoidal functions

  12. Product rule 0

  13. Product rule 0

  14. Quotient rule For the quotient , what is the derivative? Why? STOP

  15. Differentiation Derivatives and differentials Products and quotients Power rule Chain rule Sinusoidal functions

  16. Derivative of sine Recall angle-addition identity from video on trigonometry

  17. Derivative of sine 0 1 1

  18. Trigonometry: sine and cosine 1 0 -1

  19. Derivative of cosine Hint: STOP

  20. Differentiation Derivatives and differentials Products and quotients Power rule Chain rule Sinusoidal functions

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