find the derivative of 3x+4/5x^2-7x +9 with respect to x.

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$$\begin{gathered} \mathrm{y}=\frac{3\mathrm{x}+4}{5{\mathrm{x}}^2-7\mathrm{x}+9} \\ \mathrm{Differentiate} \mathrm{with} \mathrm{respect} \mathrm{to} \mathrm{x} \\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right).{\displaystyle \frac{\mathrm{d}}{\mathrm{dx}}}\left(3\mathrm{x}+4\right)-\left(3\mathrm{x}+4\right).{\displaystyle \frac{\mathrm{d}}{\mathrm{dx}}}\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right)}{{\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right)}^2} \\ =\frac{\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right).\left(3\right)-\left(3\mathrm{x}+4\right).\left(10\mathrm{x}-7\right)}{{\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right)}^2} \\ =\frac{15{\mathrm{x}}^2-21\mathrm{x}+27-\left(30{\mathrm{x}}^2+19\mathrm{x}-28\right)}{{\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right)}^2} \\ =\frac{-15{\mathrm{x}}^2-40\mathrm{x}+55}{{\left(5{\mathrm{x}}^2-7\mathrm{x}+9\right)}^2} \end{gathered}$$

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