find the derivative of the function.\ny = \\frac{9x + 7}{8x - 3}\nwhich of the following shows how to find…

find the derivative of the function.\ny = \\frac{9x + 7}{8x - 3}\nwhich of the following shows how to find the derivative of the function?\na. y=(9x + 7)(\\frac{d}{dx}(8x - 3))+(8x - 3)(\\frac{d}{dx}(9x + 7))\nb. y=(9x + 7)(\\frac{d}{dx}(9x + 7))+(8x - 3)(\\frac{d}{dx}(8x - 3))\nc. y=\\frac{(8x - 3)(\\frac{d}{dx}(9x + 7))-(9x + 7)(\\frac{d}{dx}(8x - 3))}{(8x - 3)^2}\nd. y=\\frac{(9x + 7)(\\frac{d}{dx}(8x - 3))-(8x - 3)(\\frac{d}{dx}(9x + 7))}{(9x + 7)^2}

find the derivative of the function.\ny = \\frac{9x + 7}{8x - 3}\nwhich of the following shows how to find the derivative of the function?\na. y=(9x + 7)(\\frac{d}{dx}(8x - 3))+(8x - 3)(\\frac{d}{dx}(9x + 7))\nb. y=(9x + 7)(\\frac{d}{dx}(9x + 7))+(8x - 3)(\\frac{d}{dx}(8x - 3))\nc. y=\\frac{(8x - 3)(\\frac{d}{dx}(9x + 7))-(9x + 7)(\\frac{d}{dx}(8x - 3))}{(8x - 3)^2}\nd. y=\\frac{(9x + 7)(\\frac{d}{dx}(8x - 3))-(8x - 3)(\\frac{d}{dx}(9x + 7))}{(9x + 7)^2}

Answer

Explanation:

Step1: Identify quotient - rule

For a function $y = \frac{u}{v}$, the derivative $y'=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^{2}}$. Here, $u = 9x + 7$ and $v=8x - 3$.

Step2: Apply the quotient - rule formula

$y'=\frac{(8x - 3)\frac{d}{dx}(9x + 7)-(9x + 7)\frac{d}{dx}(8x - 3)}{(8x - 3)^{2}}$.

Answer:

C. $\ y'=\frac{(8x - 3)\left(\frac{d}{dx}(9x + 7)\right)-(9x + 7)\left(\frac{d}{dx}(8x - 3)\right)}{(8x - 3)^{2}}$