What is the derivative of the function #y=sin(xy)#?

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Answer 1 · 2016-10-17T07:03:26

#dy/dx = (ycos(xy))/(1-xcos(xy))#

#d/dxy = d/dxsin(xy)#

#=> dy/dx = cos(xy)(d/dx(xy))#

#=cos(xy)[x(d/dxy)+y(d/dxx)]#

#=cos(xy)(xdy/dx + y)#

#=xcos(xy)dy/dx + ycos(xy)#

#=> dy/dx - xcos(xy)dy/dx = ycos(xy)#

#=> dy/dx(1-xcos(xy)) = ycos(xy)#

#:. dy/dx = (ycos(xy))/(1-xcos(xy))#