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Derivatives by Definition

Learn the definition of derivatives and how they represent the slope of a curve at a point. Understand the notation and theory behind derivatives, including the limit concept and formula. Explore examples to solidify your understanding.

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Derivatives by Definition

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  1. Derivatives by Definition The Long Way (no shortcuts!!)

  2. Definition The derivative is the slope of a curve at a point. Notation: y’ = f’(x)=

  3. P The Theory • If Q slides really close to P, then the slope of the secant line becomes very very close to the slope of the tangent line. What do I mean?? Q Q Q P P

  4. What is the formula? Since it’s a slope equation, its based on If we take the limit as h gets very very small (h being the x distance between P and Q) we get

  5. The Definition of a Derivative

  6. Examples

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