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By : Shagor Noor Period 6&7

AP CACLULUS AB INDIVIDUAL PROJECT DERIVATIVES . By : Shagor Noor Period 6&7. What are derivatives? According to Merriam Webster dictionary, the derivative is the “  the limit of the ratio of the change in a function to the corresponding change in its independent variable.”

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By : Shagor Noor Period 6&7

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  1. AP CACLULUS AB INDIVIDUAL PROJECT DERIVATIVES By : Shagor Noor Period 6&7

  2. What are derivatives? According to Merriam Webster dictionary, the derivative is the “ the limit of the ratio of the change in a function to the corresponding change in its independent variable.” In other words, the derivative is the instantaneous rate of change; which is basically the slope of an equation.

  3. Finding the Derivative In order to find the derivative, one must first know all the derivative formulas… which are:

  4. The Three Most Important Derivative Rules Are • The Quotient Rule • The Product Rule • And the Chain Rule

  5. Quotient Rule You use this rule when you are trying to find the derivative of an equation that is in fraction form. Just remember : Lowdihigh – HighdiLow over Lowlow

  6. Product Rule The way I solve for the product rule is that I always tell myself “keep, derivative plus derivative times keep” This means you keep the first equation and multiply that by the derivative of the second equation and then you add that to the derivative of the second equation times the first equation.

  7. Chain Rule In order to do the chain rule, you find the derivative of the outside function first and then you multiply that by both the derivative of the inside function and its derivative. Example: (2x + 1) ^ 2 2(2x + 1 ) * 2 = 4(2x + 1) = 8x + 4

  8. An Easy Way Out An easy way to solve for the derivative is by using your graphing calculator. First you plug in the equation into your calculator and then press 2nd Trace [6] . This allows you to find the derivative of the equation at a particular x coordinate.

  9. What are Antiderivatives ? Antiderivatives are the inverse operation of differentiation. Basically you are working backwards to solve for the original equation if you are given the derivative. In addition, if you are given a graph, the antiderivative helps you to find the area underneath the curve.

  10. Formulas you need to know for Integration!

  11. Area In order to find the area underneath the curve, you have to integrate the value of the top function minus the bottom function. For example: Find the area between the equations x^2 and X +2

  12. First you find your upper and lower limits by finding the x – coordinates that they both share. This would be -1 and 2. Then you set up an equation that involves integration. Since X+2 is on the top, this would be your “top” function. Then you subtract by x^2 which is your “bottom” function. Your equation would be: And the answer should be 4.5

  13. Citation Page http://www.merriam-webster.com/dictionary/derivative http://www.schooltutoring.com/help/wp-content/uploads/Quo-rule-expl.png http://www.chegg.com/homework-help/definitions/antiderivatives-29 http://www.cantonschools.org/~lforastiere/00F5BEEB-0075833E.1/Captain%20Calculus.jpg http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html http://www.keepcalmstudio.com/_gallery/300/S7hDvO.png

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