# How do you find the derivative of 1/x+1/y=7?

Nov 20, 2016

${x}^{-} 1 + {y}^{-} 1 = 7$

$- 1 {x}^{-} 2 - {y}^{-} 2 \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$- {y}^{-} 2 \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = \frac{1}{x} ^ 2$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{1}{x} ^ 2}{- \frac{1}{y} ^ 2}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {y}^{2} / {x}^{2}$

Hopefully this helps!