# How do you use implicit differentiation to find dy/dx given (x^2+y^2)^99=alpha?

Sep 25, 2016

$- \frac{x}{y}$

#### Explanation:

Given $f \left(x , y\right) = 0$

${f}_{x} \mathrm{dx} + {f}_{y} \mathrm{dy} = 0$ so $\frac{\mathrm{dy}}{\mathrm{dx}} = - {f}_{x} / {f}_{y}$

Here

${f}_{x} = 198 x {\left({x}^{2} + {y}^{2}\right)}^{98}$
${f}_{y} = 198 y {\left({x}^{2} + {y}^{2}\right)}^{98}$

then

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{x}{y}$