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Derivatives

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Derivatives

1. 1. Derivatives <br />By: Kyle Shaffer <br />
2. 2. What is a dervitive?<br />Is the instantaneous change of one quantity to another <br />-Original equation<br />-Derivative of the <br />equation<br />
3. 3. How is a derivative linked to limits?<br />Limits are used to find derivatives <br />
4. 4. What is the definition for a limit, and what does it mean? <br />a Limit means to find what value y is as x approaches a certain number. This means a limit exists when the limit value is approached from both sides equally from the left and right side. If the arrow is going up to infinity next to the asymptote and the other side the arrow is going down negative infinity they do not exist.<br />
5. 5. Types of derivatives: Power Rule<br />The power rule can be used to find the derivative by multiplying the exponent by the coefficient, and writing the new exponent as the old one minus 1. This can be used for multiple quantities as long as they are being added or subtracted, not multiplied or divided.<br /> -Original equation<br />-power rule<br />
6. 6. Chain Rule<br />you use the chain rule when you see exponents around two quantities in parentheses or if I see a trig angle that is more than just (x). To use the chain rule you find the derivative of the outside and then multiply it by the derivative of the inside.<br />
7. 7. Quotient Rule <br />the quotient rule is used to find derivatives when quantities are being divided. So when you see a fraction, you will most likely be using the quotient rule. A catchy way to remember the quotient Rule formula: <br />
8. 8. Product Rule<br />The product rule is used to find the derivative when you cannot use the power rule because two things are being multiplied. You use the formula:<br />
9. 9. Implicit Rule<br />Is when you have x’s and y’s in a equation. You then substitute dx/dy and dx/dx in for your x’s and y’s. Then you try to get dy/dx by itself.<br />
10. 10. Implicit Rule Example <br />