Find the differential, $LaTeX: \displaystyle dy$ , of $LaTeX: \displaystyle y = \sqrt{5 x^{2} + 8}$ .

The differential is given by $LaTeX: \displaystyle dy = f'(x)dx$ . Using the formula gives: $LaTeX: dy = \frac{5 x}{\sqrt{5 x^{2} + 8}}\,dx$