Answer
$$y'=-2(2x-5)^{-2}(x^2-5x)^6+6(x^2-5x)^5$$
Work Step by Step
$$y=(2x-5)^{-1}(x^2-5x)^6$$
The derivative of $y$ is: $$y'=\Big((2x-5)^{-1}\Big)'(x^2-5x)^6+(2x-5)^{-1}\Big((x^2-5x)^6\Big)'$$
$$y'=-(2x-5)^{-2}(2x-5)'(x^2-5x)^6+(2x-5)^{-1}\Big(6(x^2-5x)^5(x^2-5x)'\Big)$$
$$y'=-2(2x-5)^{-2}(x^2-5x)^6+6(2x-5)^{-1}(x^2-5x)^5(2x-5)$$
$$y'=-2(2x-5)^{-2}(x^2-5x)^6+6(x^2-5x)^5$$