Solution — 2021 Question 2 Differentiation & Applications| Integration & Applications

$$\begin{array}{cc}y& ={(2x^3-5x^{\frac{1}{3}})}^2\\ & =4x^6-20x^{\frac{10}{3}}+25x^{\frac{2}{3}}\\ \frac{\mathrm{d}y}{\mathrm{d}x}& =24x^5-\frac{200}{3}{x}^{\frac{7}{3}}+\frac{50}{3}{x}^{-\frac{1}{3}}\\ & =24x^5-\frac{200}{3}{x}^{\frac{7}{3}}+\frac{50}{3x^{\frac{1}{3}}}∎\end{array}$$

$$\begin{array}{cc}& {\displaystyle \int \frac{1}{\sqrt{5-4x}}\mathrm{d}x}\\ & ={\displaystyle \int {(5-4x)}^{-\frac{1}{2}}\mathrm{d}x}\\ & =-\frac{{(5-4x)}^{\frac{1}{2}}}{2}+c∎\end{array}$$