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.

## Answer This Question

## Related Questions

- Calculus - Find the derivative of the function y defined implicitly in terms of ...
- calculus - A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...
- Calculus (Please check my work!) - Suppose that y = f(x) = x^2 - 4x + 4. Then on...
- Calculus - A function is implicitly defined by x^2 - 4y^2 = 9 Find the equation ...
- AP calculus - Find (dy/dx) for the following implicitly defined function: 2x = ...
- calculus - suppose a price-demand function p(x) is defined implicitly by x= p^3-...
- AP Calculus - Consider a curve given implicitly by the equation (1+x)y^3 + (x^4)...
- AP Calculus - Find (dy/dx) for the following implicitly defined function: cos(x-...
- calculus - Find the length of the arc formed by y = (1/8)(4x^2-2ln(x)) from x=4 ...
- Calculus 2 (Differential Equation) - How would you solve the following problem ...

More Related Questions