Find the differential, $LaTeX: \displaystyle dy$ , of $LaTeX: \displaystyle y = \sqrt{4 x^{5} + 5}$ .

The differential is given by $LaTeX: \displaystyle dy = f'(x)dx$ . Using the formula gives: $LaTeX: dy = \frac{10 x^{4}}{\sqrt{4 x^{5} + 5}}\,dx$