# How do you use implicit differentiation to find (dy)/(dx) given 2x^3=2y^2+5?

May 21, 2017

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

$\frac{d}{\mathrm{dx}} \left(2 {x}^{3}\right) = \frac{d}{\mathrm{dx}} \left(2 {y}^{2} + 5\right)$

$6 {x}^{2} = 4 y \frac{\mathrm{dy}}{\mathrm{dx}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 {x}^{2}}{2 y}$