Find dy/dx for 2 + xy = x. please show your work

Answer 1

Differentiate implicitly

x dy/dx + y = 1

x dy/dx = 1-y

dy/dx = (1-y) / x

Answer 2

xy' + y = 1

y' = (1-y)/x, 2+xy= x, xy= x-2, y= 1-2/x

y' = (1-1 -(-2/x))/x = 2/x/x

y' = dy/dx = 2/x^2

y' = dy/dx = 2/x^2

derivative of a constant = 0. d(2)/dx=0

derivative of xy is the derivative of x times y + the derivative of y times x. the derivative of a product is the derivative of first term times the 2nd term plus derivative of the 2nd term times the 1st term

dx/dx = 1

an alternative method is:

2 +xy =x could be rewritten as

2/x + y = 1 by dividing by x

then separate the variables, solve for y

y= 1- 2/x

take the derivative

dy/dx = y' = d(-2x^-1)dx = 2x^-2 = 2/x^2

dy/dx = 2/x^2