Example 11. $y=\frac{(x+2)^{2}}{(x-1)^{3}(x+5)^{4}}$.
Solution. First, we find $\ln y$, then differentiate both sides of the obtained equation, where the left side $\ln y(x)$ is differentiated as a composite function: $\ln y=2 \ln (x+2)-3 \ln (x-1)-4 \ln (x+5)$ and $\frac{1}{y} y^{\prime}=\frac{2}{x+2}-\frac{3}{x-1}-\frac{4}{x+5} ;(\ln y)^{\prime}=\frac{1}{y} y^{\prime}-$ the derivative of a composite function. From this, $y^{\prime}=\frac{(x+2)^{2}}{(x-1)^{3}(x+5)^{4}} \cdot\left(\frac{2}{x+2}-\frac{3}{x-1}-\frac{4}{x+5}\right)$.