This past week we reviewed a lot on derivatives and we will have a lot of them on the Exam this coming week so I'll blog on Product and Quotient Rule to review the two...
-Product Rule :
f( x ) g( x ) = f( x ) g’( x ) + g( x ) f’( x ) ( copy 1st ) ( derivative 2nd ) + ( copy 2nd ) ( derivative 1st )
Ex. g( x ) = ( 3x^2+4 ) ( 2x^2-3x )
= ( 3x^2+4 ) ( 4x-3 ) - ( 2x^2-3x ) ( 6x )
= 12x^3 - 9x^2 + 16x - 12 - 12x^3 + 9x^2
= 16x - 2
-Quotient Rule :
f (x ) / g( x ) = g( x ) f’( x ) – [ f( x ) g’( x ) ] / ( g( x ) )^2 ( copy bottom ) ( derivative top ) – [ ( copy top ) ( derivative bottom ) ] / ( bottom )^2
You solve the same way with the quotient rule, following the steps ( formula ) and when simplifying, if there is a trig identity in the answer use the identity to simplify the answer completely.
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