How to find the derivative of implicit function? For the derivative of the implicit function e ^ y + xy-e = 0, both sides of the equation derive from X: D / DX (e ^ y + xy-e) = e ^ y (dy / DX) + y + X (dy / DX). Why is x (dy / DX) derived from e? Shouldn't it be 0? There is another derivative from y ^ 2-2xy + 9 = 0: 2yy '- 2Y + 2XY' = 0? Why does 9 become 2XY '? Where do you get 2XY' from? I don't understand```````````````

How to find the derivative of implicit function? For the derivative of the implicit function e ^ y + xy-e = 0, both sides of the equation derive from X: D / DX (e ^ y + xy-e) = e ^ y (dy / DX) + y + X (dy / DX). Why is x (dy / DX) derived from e? Shouldn't it be 0? There is another derivative from y ^ 2-2xy + 9 = 0: 2yy '- 2Y + 2XY' = 0? Why does 9 become 2XY '? Where do you get 2XY' from? I don't understand```````````````

The essence of the so-called implicit function is that y is a function of X, and X is an independent variable. In the first question, y + X (dy / DX) is the result of XY deriving from X. This is the result of multiplication of two functions (UV) '= u'v + UV', and the derivative of E is 0. The second question is the same, and - 2Y + 2XY 'is derived from the derivation of - 2XY