Find y ′ by implicit differentiation. x * e^y = y * sinx

Answer 1

Will need to use the product rule

(1)(e^y) +(x)(e^y)dy/dx =dy/dx(sin x) +ycos(x) Now put all the dy/dx terms on one side of the equation

x(e^y)dy/dy -dy/dx(sinx)= ycos(x) -e^y factor dy/dx out of both terms on the left

dy/dx( xe^y - sinx) = ycos(x) -e^y

dy/dx= (ycosx-e^y)/(xe^y -sinx)

There you go