# How do you use implicit differentiation to find (dy)/(dx) given 16x^2+25y^2=400?

Jan 24, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{16 x}{25 y}$

#### Explanation:

Differentiate both sides of the equation with respect to $x$:

$\frac{d}{\mathrm{dx}} \left(16 {x}^{2} + 25 {y}^{2}\right) = 0$

$32 x + 50 y y ' = 0$

$y ' = - \frac{16 x}{25 y}$