Expert: Ahmed Salami - 10/21/2008

Question
Can you show me how to find the derivative of yx^1/2 - xy^1/2 = 16 implicitly?

Answer
Hi Starla,
The trick to implicit differentiation is to always add dy/dx after
differentiating any expression in y. We'll be using the product rule
here.
yx^1/2 - xy^1/2 = 16
[y(1/2)x^-1/2 + x^1/2.1.dy/dx] - [x(1/2)y^-1/2.dy/dx + y^1/2.1] = 0
(1/2)yx^-1/2 + x^1/2(dy/dx) - (1/2)xy^-1/2(dy/dx) - y^1/2 = 0
x^1/2(dy/dx) - (1/2)xy^-1/2(dy/dx) = y^1/2 - (1/2)yx^-1/2
(dy/dx)[x^1/2 - (1/2)xy^-1/2] = y^1/2 - (1/2)yx^-1/2
dy/dx = [y^1/2 - (1/2)yx^-1/2] / [x^1/2 - (1/2)xy^-1/2]

You can always get back to me if anything is unclear.
Regards.