высшая-математика - Найти производную функцию по определению производной

$$\begin{array}{l} y\left( x \right) = \frac{5}{{4x + 3}}\\ y'\left( x \right) = \mathop {\lim }\limits_{h \to 0} \frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\\ \frac{{f\left( {x + h} \right) - f\left( x \right)}}{h} = \frac{{\frac{5}{{4\left( {x + h} \right) + 3}} - \frac{5}{{4x + 3}}}}{h} = \\ 5 \cdot \frac{{ - 4h}}{{h\left( {4\left( {x + h} \right) + 3} \right)\left( {4x + 3} \right)}} = \frac{{ - 20}}{{\left( {4\left( {x + h} \right) + 3} \right)\left( {4x + 3} \right)}} \Rightarrow \\ y'\left( x \right) = \mathop {\lim }\limits_{h \to 0} \frac{{ - 20}}{{\left( {4\left( {x + h} \right) + 3} \right)\left( {4x + 3} \right)}} = - \frac{{20}}{{{{\left( {4x + 3} \right)}^2}}} \end{array}$$