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math:derivative [2021/09/16 14:48] – Filled out alt form epixmath:derivative [2021/09/16 15:01] (current) – made image look better epix
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 A derivative is valid when the function is [[math:limits|continuous]] and when it is differentiable, meaning that both sides of a function approaches the same slope at any given point. If not, this means that there is either a cusp, corner, or vertical tangent present. A derivative is valid when the function is [[math:limits|continuous]] and when it is differentiable, meaning that both sides of a function approaches the same slope at any given point. If not, this means that there is either a cusp, corner, or vertical tangent present.
  
-{{ :math:der6.gif?400 |}}+{{:math:der6.gif|}}
  
   * A cusp is present when each side of a function approaches a vertical slope, which Does Not Exist.   * A cusp is present when each side of a function approaches a vertical slope, which Does Not Exist.
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   * A discontinuity means that the slope function is also has a discontinuity, which prevents a continuous derivative.   * A discontinuity means that the slope function is also has a discontinuity, which prevents a continuous derivative.
 ===== Calculating the Derivative ===== ===== Calculating the Derivative =====
-{{ :math:tangent_animation.gif|}}+[{{ :math:tangent_animation.gif?400|$\Delta x$ in this visualization is the same as $h$ in the definition of a limit}}]
 Using the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$, you can derive the definition of a derivative using a limit. Using the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$, you can derive the definition of a derivative using a limit.
  

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