Product and Quotient Rule Wksht

Calculus ConceptsProduct/Quotient Rule WorksheetName:Date:ddxProduct Rule: ( )f( x) g( x) = f( x) g'( x) + g( x) f '( x)d ⎛ f( x) ⎞ g( x) f '( x) − f( x) g'( x) Quotient Rule: ⎜ ⎟= 2 , where gx ( ) ≠ 0dx ⎝ g( x) ⎠ ( g( x))Directions: Find the derivative of each problem using either the product or the quotient rule.Show all calculus and algebra necessary to arrive at your answer. NO CALCULATORS.PRACTICE PROBLEMS (IN CLASS)A. Find h'( x)if2hx ( ) = (3x− 2 x)(5+ 4 x)B. Find g'( x)if gx ( ) = xsinxdC. Find ( f ( x ))dx15x− 2= − D. Find f '( x)if f( x)=23x + 1if f( x) ( 2x3 4)

E. Find g'( x)if13 −gx ( ) = xF. Find h'( x)ifx + 51−coshx ( ) =sin xHOMEWORK PROBLEMS: Find the derivative of each of the following functions using theproduct or quotient rule. Show all necessary calculus and algebra used to arrive at your answer.1.2.3.4.f x x x x2 3( ) = ( − 2 + 1)( − 1)x 1f( x)= +x − 12f( x) = x cosxf( x) = sinxcosx5.f( x)=x + 1x6.7.8.2x+ 3f( x)=6f x x x x x3 2( ) = ( − 3 )(2 + 3 + 5)sin xf( x)=cos x