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Eile Edit View Higtory Bookmarks Iools Help Section 25 e Chegg Study | Guided Soluti x w Mathway | Math Problem Sc w Blackboard Learn Review Test submission: Prc writcriticalessaylit.pdf × X € www.webassign.net/web/ tudent/Assignment.R it?dep-17019169 1. 01 points | Previous Answers Ic11 2.5.010. 115 Submissions Used My Notes Ask Your Find dy/dx by implicit differentiation dy/dx = Need Help? eaItTalk to a Tutor Submit Answer Save Progress 2. +-1 points LarCalc11 2.5.012. 015 Submissions Used My Notes Ask Your Find dy/dx by implicit differentiation. dy/dx = Need Help?dWatch Talk to a Tutor 3. ÷ -M points LarCalc11 2.5.508 XP 0/5 Submissions Used My Notes Ask Your Teacher Find dy/dx by implicit differentiation. 2 cos (6x) sin (6y) 1

Explanation / Answer

1)

8x2y +2y2x =-4

differentiate with respect to x on both sides . product rule:(uv)'=u'v +uv'

((8*2x2-1y(dx/dx)) +(8x2(dy/dx))) +((2*2y2-1x(dy/dx))+(2y2(dx/dx))) =d(-4)/dx

=>((16xy*1) +(8x2(dy/dx))) +((4yx(dy/dx))+(2y2*1)) =0

=>16xy +(8x2(dy/dx)) +(4yx(dy/dx))+2y2 =0

=>(8x2 +4yx)(dy/dx) =-(2y2+16xy)

=>(dy/dx) =-(2y2+16xy)/(8x2 +4yx)

=>(dy/dx) =-(y2+8xy)/(4x2 +2xy)

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2)

(xy)=x9y +58

=>(xy)=x9y +58

differentiate with respect to x on both sides

=>((1/2x)y(dx/dx))+(x(1/2y)(dy/dx))=(9x8y(dx/dx))+(x9(dy/dx)) +0

=>((1/2)(y/x))+((1/2)(x/y)(dy/dx))=(9x8y)+(x9(dy/dx))

=>((1/2)(x/y)(dy/dx))-(x9(dy/dx)) =(9x8y)-((1/2)(y/x))

=>((1/2)(x/y) -x9)(dy/dx) =(9x8y)-((1/2)(y/x))

=>((x/y)   -2x9)(dy/dx) =(18x8y)- (y/x)

=>x(x -2x9y)(dy/dx) =((18x8xy)- y)y

=>(x -2x9(xy))(dy/dx) =((18x8y(xy))- y)

=>(dy/dx) =((18x8y(xy))- y)/(x -2x9(xy))

=>(dy/dx) =((18x7(xy)3/2)- y)/(x -2x9(xy))

=>(dy/dx) =-(y -(18x7(xy)3/2))/(x -2x9(xy))

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3)

2cos(6x) sin(6y) =1

differentiate with respect to x on both sides

(2(-sin(6x))(6dx/dx) sin(6y))+(2cos(6x) cos(6y) (6dy/dx))=0

=>(-12sin(6x)sin(6y))+(12cos(6x) cos(6y) (dy/dx))=0

=>(12cos(6x) cos(6y) (dy/dx))=(12sin(6x)sin(6y))

=>(dy/dx)=(12sin(6x)sin(6y))/(12cos(6x) cos(6y))

=>(dy/dx)=tan(6x)tan(6y)

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