implicit differentiation help

Hey everyone:

I am having some trouble with this problem. I think I am having a problem with the algebra.

$\displaystyle
\sqrt {xy} = 1 + x^2y
$


I can get to this point
$\displaystyle
\frac1 2(xy)(y + x\frac{dy}{dx}) = 2xy + x^2\frac{dy}{dx}
$

I'm having some difficulty getting passed this.

Any help is appreciated.

Thanks

Quote:

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Originally Posted by evant8950

Hey everyone:

I am having some trouble with this problem. I think I am having a problem with the algebra.

$\displaystyle
\sqrt {xy} = 1 + x^2y
$


I can get to this point
$\displaystyle
\frac1 2(xy)(y + x\frac{dy}{dx}) = 2xy + x^2\frac{dy}{dx}
$

I'm having some difficulty getting passed this.

Any help is appreciated.

Thanks

---

$\displaystyle
\sqrt {xy} = 1 + x^2y
$

$\displaystyle
\frac1 2(xy)^{-\frac{1}{2}}(y + x\frac{dy}{dx}) = 2xy + x^2\frac{dy}{dx}
$