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Remember this?

Remember this?. Derivative. Finding the derivative = differentiating. If you are asked to “differentiate a function”, what you are really being asked to do is find the limit of your difference quotient (what we’ve been doing all along). Example Definition of Derivative. Notation.

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Remember this?

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  1. Remember this?

  2. Derivative

  3. Finding the derivative = differentiating • If you are asked to “differentiate a function”, what you are really being asked to do is find the limit of your difference quotient (what we’ve been doing all along).

  4. Example Definition of Derivative

  5. Notation

  6. does not mean ! does not mean times ! does not mean ! Note: dx does not mean d times x ! dy does not mean d times y !

  7. Differentiable Function

  8. Example

  9. What if we call Q something else?

  10. Derivative - Alternate Derivative - Alternate

  11. Example

  12. Notations for Derivative • y’, y”, y’’’, y(4) • dy/dx, d2y/dx2, d3x/dx3 • f ‘(x), f “(x), f “‘(x), f (4)(x) • Dx, Dx2, Dx3,

  13. One-sided Derivatives

  14. One-sided Derivatives

  15. Example One-sided Derivatives

  16. Example

  17. Derivative = slope of tangent lines…right? If you are SUPER lucky, your function won’t be a curved graph. If it is made up of straight lines, the derivative is just a function of the individual slopes…

  18. The derivative is the slope of the original function. The derivative is defined at the end points of a function on a closed interval.

  19. A function is differentiable if it has a derivative everywhere in its domain. It must be continuous and smooth. Functions on closed intervals must have one-sided derivatives defined at the end points. p

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