Differentiate with respect to x to the given function`(3x+4)/(5x^(2)-7x+9)`

Explanation

To differentiate the function \( y = \frac{3x + 4}{5x^2 - 7x + 9} \) with respect to \( x \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

\[ \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \]

where \( u = 3x + 4 \) and \( v = 5x^2 - 7x + 9 \).

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