for 4 + xy = y
Tabitha D. answered • 01/04/20
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With implicit differentiation, just differentiate each term, but when you differentiate y, you have an extra dy/dx.
4 + xy = y2
Use the product rule on the left, and the power rule on the right:
0 + x(1) dy/dx + (1)y = 2y dy/dx
x dy/dx + y = 2y dy/dx
Get everything with dy/dx on one side and everything without it on the other side:
y = 2y dy/dx - x dy/dx
Factor out dy/dx:
y = (2y - x) dy/dx
Divide both sides to get dy/dx by itself:
dy/dx = y/(2y - x)
