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

1 Answer
Steve M
Jan 19, 2018

# dy/dx = (y - 1)/(2-x) #

Explanation:

We have:

# x + 2y = xy #

If we differentiate wrt #x# and apply the product rule then:

# d/dx (x) + d/dx (2y) = x(d/dx y)+(d/dx x)(y) #

# :. 1 + 2dy/dx = xdy/dx + (1)y#

# :. 2dy/dx - xdy/dx = y - 1 #

# :. (2-x) dy/dx = y - 1 #

# :. dy/dx = (y - 1)/(2-x) #

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