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?

Lzr0 said:

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?

Click to expand...

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.

Subhotosh, many thanks.
Lazar