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

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

#1**+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

CPhill Mar 28, 2018