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\(sin(xy)=x+y\)

I'm having loads of trouble figuring out implicit derivatives.
Could someone please work out this problem in great detail? I'm a slow learner on hard stuff
Thanks so much

StayCurly  Mar 28, 2018
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1+0 Answers

 #1
avatar+85673 
+1

sin (xy)  = x + y

 

Use the Chain Rule on the left

 

cos(xy) *[ xy' +  y ]  =  1  + y'

 

cos(xy) * xy' + cos(xy)*y  =  1 + y'      ....collect the y' terms on the left.....

 

xy' cos(xy) - y'  =   1  -  y* cos(xy)

 

y '   [ x*cos (xy)  - 1 ]  =  1 - y* cos(xy)

 

y ' =    [  1  - y* cos(xy) ]

          _____________

              x* cos(xy) - 1

 

 

cool cool cool

CPhill  Mar 28, 2018

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