Answer
The Derivative is:
$w'=-\frac{17}{(2x-7)^2}$
Work Step by Step
$w=(2x-7)^{-1}(x+5)$
$w=\frac{x+5}{2x-7}$
Using Quotient Rule to find the Derivative:
$w'=\frac{f'(x)\cdot g(x) - f(x)\cdot g'(x)}{g^2(x)}$
$w'=\frac{((1)x^{1-1}+0)(2x-7)-(x+5)(2x^{1-1}-0)}{(2x-7)^2}$
$w'=\frac{(1)(2x-7)-(x+5)(2)}{(2x-7)^2}$
$w'=\frac{2x-7-2x-10}{(2x-7)^2}$
$w'=-\frac{17}{(2x-7)^2}$
