# Thread: Finding derivative dy/dx when y(x) is defined indirectly by an equation

1. ## Finding derivative dy/dx when y(x) is defined indirectly by an equation

Hi,
I feel embarrassed, but I forgot how to derive dY/dX when a function Y(X) is defined indirectly via an equation.
For example, I have: X=Y*(Y+A)/B, where A and B are contstants. How do I find dY/dX?

2. Originally Posted by Lzr0
Hi,
I feel embarrassed, but I forgot how to derive dY/dX when a function Y(X) is defined indirectly via an equation.
For example, I have: X=Y*(Y+A)/B, where A and B are constants. How do I find dY/dX?
That is called implicit differentiation. You would need to use chain rule and product rule (mostly).

But for this problem (Quadratic equation), you can write:

Y = [-A ± √(A2 + 4BX)]/2

and carry-out straight-forward differentiation.

3. Subhotosh, many thanks.
Lazar

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