Posted by **Anonymous** on Friday, June 22, 2012 at 8:24am.

Find the derivative of the function y defined implicitly in terms of x.

y = sqrt(xy + 9)

Please help! Thanks! :)

- Calculus -
**Reiny**, Friday, June 22, 2012 at 8:55am
Did you mean "with respect to x" ?

If so then I would square both sides

y^2 = xy + 9

2y dy/dx = x dy/dx + y

2y dy/dx - x dy/dx = y

dy/dx(2y-x) = y

dy/dx = y/(2y-x) such that √(xy-9) ≥ 0

if you want that expression to be in terms of x only, (like you typed)

we have a mess ahead

we would have to solve

y^2 - xy - 9 = 0 for y in terms of x

y = (x ± √(x^2 +36) )/2

and sub that into dy/dx to get only x's

so I will wait for your clarification before I start that messy substitution.

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