Product+Rule

  Power Rule | Quotient Rule | Chain Rule

__DEFINITION__: The product of two differntiable functions is the first function times the derivative of the second, plus the second function times the derivative of the first...

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<span style="FONT-FAMILY: 'Trebuchet MS',Helvetica,sans-serif"><span style="FONT-FAMILY: Georgia,serif"><span style="FONT-FAMILY: 'Trebuchet MS',Helvetica,sans-serif"><span style="BACKGROUND-COLOR: rgb(253,225,255)"><span style="FONT-SIZE: 120%; COLOR: rgb(121,22,109)"> __IN OTHER WORDS__: The derivative of the function (FG) is equal to the derivative of F times G plus F times the derivative of G.       <span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)">

<span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)"> <span style="COLOR: rgb(249,148,148); BACKGROUND-COLOR: rgb(210,20,20)">__EXAMPLE__: <span style="DISPLAY: block; FONT-SIZE: 110%; FONT-FAMILY: 'Comic Sans MS',cursive; BACKGROUND-COLOR: rgb(255,250,77); TEXT-ALIGN: left"><span style="BACKGROUND-COLOR: rgb(255,255,255)"><span style="BACKGROUND-COLOR: rgb(255,255,255)"><span style="BACKGROUND-COLOR: rgb(255,255,255)"> <span style="COLOR: rgb(189,177,15)"><span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)">     f(x) = a b f(x) = 2x (2x - 2) f'(x) = <span style="COLOR: rgb(15,245,26)">a' b + a<span style="COLOR: rgb(214,8,5)"> b' f'(x) = (<span style="COLOR: rgb(32,222,13)">2 ) (2x - 2) + (2x) ( 2 ) f'(x) = (4x - 4) + (4x) f'(x) = (8x - 4) or (4) (2x - 1) <span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)"> <span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)">

<span style="FONT-FAMILY: 'Courier New',Courier,monospace"> <span style="COLOR: rgb(224,105,21)"><span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)"><span style="FONT-SIZE: 110%; COLOR: rgb(231,99,4)"><span style="BACKGROUND-COLOR: rgb(200,241,254)"><span style="BACKGROUND-COLOR: rgb(250,214,153)"> __APPLICATION__: media type="custom" key="641797" <span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)">

<span style="BACKGROUND-COLOR: rgb(17,167,238)"><span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)"><span style="COLOR: rgb(8,20,201); FONT-FAMILY: Impact,Charcoal,sans-serif">__LINKS__: <span style="BACKGROUND-COLOR: rgb(255,255,255)"><span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)"> <span style="COLOR: rgb(36,0,158)">[|Product rule examples and explanation] <span style="COLOR: rgb(36,0,158)">[|Product rule drills] <span style="COLOR: rgb(36,0,158)">[|Product rule movie]   <span style="COLOR: rgb(240,112,112); BACKGROUND-COLOR: rgb(255,255,255)"><span style="BACKGROUND-COLOR: rgb(255,255,255)"><span style="COLOR: rgb(36,0,158)">