Question

Find dy/dx by implicit differentiation for x + 2y = xy.

Answer 1

Ok to find dy/dx of x+2y=xy we take derivative of both sides with respect to x

1+2dy/dx = x*dy/dx +y*dx/dx
1+ 2dy/dx = x*dy/dx + y* 1
2dy/dx +1 = x*dy/dx + y

2y’ + 1 = xy’ + y

2y’ + 1 - xy’ = y

2y’ -xy’ = y - 1

y’(2-x) = y - 1

so we get finally

y’= (y-1)/(2-x)

Hope this helps you understand the concept! Any questions please ask! Thank you so much!!