APFIVE Implicit Differentiation
For the implicit equation $$x^2+y^2+2*\sqrt{x*y}=10$$, differentiate implicitly to find an expression for $$\frac{dy}{dx}$$.
| x | y |
|---|---|
| 1.0 | 2.5 |
| 2.0 | 2.0 |
| 3.0 | 1.5 |
A
$$\frac{dy}{dx}=\frac{-2*x+\frac{y}{\sqrt{x*y}}}{2*y-\frac{x}{\sqrt{x*y}}}$$
B
$$\frac{dy}{dx}=-\frac{2*x+\frac{y}{\sqrt{x*y}}}{2*y+\frac{x}{\sqrt{x*y}}}$$
C
$$\frac{dy}{dx}=\frac{-2*x-\frac{y}{\sqrt{x*y}}}{2*y+\frac{x}{\sqrt{x*y}}}$$
D
$$\frac{dy}{dx}=\frac{2*x+\frac{y}{\sqrt{x*y}}}{2*y+\frac{x}{\sqrt{x*y}}}$$
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