3.31: Derivative of a quotient, small change, and ln integral

Given $f(x) = \dfrac{3x + 4}{2x - 5}$ for $x \neq \dfrac{5}{2}$, find $f'(x)$ as a simplified algebraic fraction.

Variables $x$ and $y$ are related by $y = 3x + \dfrac{2}{x} + 5$. Using differentiation, find the approximate change in $x$ when $y$ increases from $10$ by $0.01$.

Differentiate $y = x^{3}\ln x$ with respect to $x$.

Hence find $\displaystyle\int (6x^{2}\ln x + 2x^{2})\,\mathrm{d}x$.