Chapter 1.5 Lecture Notes
Chapter 1.5 Lecture Notes STAT 1102 - 003
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This 3 page Class Notes was uploaded by Kayla Notetaker on Saturday September 26, 2015. The Class Notes belongs to STAT 1102 - 003 at Temple University taught by Ron Kershner in Fall 2015. Since its upload, it has received 45 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.
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Date Created: 09/26/15
C15 Differentiation Techniques Derivatives are functions How do we write them dy Y or f x or dx These are all different ways to write the same thing Trigger words for finding derivatives quotRate of Change quotSlope of a tangent line Rules for Determining Derivatives 1 Power rule Y xk K any positive negative or fractional number To take the derivative pull K down from the exponent and make it the coefficient to x then subtract 1 from K YK 4 Examples Basic functions Yx2 Y 2x2391 Y 2x1 Y 2x Radical functions Y x Turn radicals into rational functions Y x turns into y x12 Now take the derivative Y 12 X1 1 Y 12 x39 2 Y 12x Fraction derivatives Y lx Put x in numerator Y x391 Use power rule Y 1 x39l391 Y 1x392 Y 1x2 Derivative of a Constant Y 10 Y 0 Remember that a derivative is the slope and y equal to a constant means the line is horizontal Horizontal lines do not have slopes Derivative of a Constant times a Function Gx cfx gt ddx gx c ddx fx The derivative of a constant times a function is the constant number times the derivative of the function Example Y 10x2 Y 10 2x2391 Y 10 2x Y 20x Derivative of a Sum or Difference derivative of fx the derivative of gx Example ddx5x3 7 ddx5x3 ddx7 ddx 53x3391 ddx0 ddx 15x2 0 The derivative of 5x3 7 15x2 Slopes of Tangent Lines The slope of a tangent line of fx at x a IS the derivative of fx evaluated at x a Example Fx x3 6x2 at x 6 ddx 3x3391 ddx 6 2x2391 ddx 3x2 12x plug in 6 to find slope of tangent line at x 6 362 126 312 72 36 72 36 The slope of tangent line at x 6 of Fx x3 6x2 is 36
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