What is the implicit derivative of #1= e^y-xcos(xy) #?

1 Answer
Oct 12, 2016

#(dy)/dx=(cosxy-xysinxy)/(e^y+x^2(sinxy))#

Explanation:

#1=e^y−xcos(xy)#
#rArr(d1)/dx=d/dx(e^y−xcos(xy))#
#rArr0=(de^y)/dx-(d(xcos(xy)))/dx#
#rArr0=(dy/dx)e^y-(((dx)/dx)cosxy+x(dcosxy)/dx)#
#rArr0=(dy/dx)e^y-(cosxy+x(dxy)/dx(-sinxy))#
#rArr0=(dy/dx)e^y-(cosxy+x((y+x(dy)/dx)(-sinxy)))#
#rArr0=(dy/dx)e^y-(cosxy+x(-ysinxy-x(dy)/dx(sinxy)))#
#rArr0=(dy/dx)e^y-(cosxy-xysinxy-x^2(dy)/dx(sinxy))#
#rArr0=(dy/dx)e^y-cosxy+xysinxy+x^2(dy)/dx(sinxy)#
#rArr0=(dy/dx)e^y+x^2(dy)/dx(sinxy)-cosxy+xysinxy#
#rArr0=(dy/dx)(e^y+x^2(sinxy))-cosxy+xysinxy#
#rArrcosxy-xysinxy=(dy/dx)(e^y+x^2(sinxy))#

#rArr(dy)/dx=(cosxy-xysinxy)/(e^y+x^2(sinxy))#