# How do you differentiate (x^2)-2xy+y^3?

Aug 10, 2015

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

#### Explanation:

By implicit differentiation each term differentiates to:

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

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

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

Combing these terms we have:

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