Answer
$$y'=6(5-2x)^{-4}-x^{-2}\Big(\frac{2}{x}+1\Big)^3$$
Work Step by Step
$$y=(5-2x)^{-3}+\frac{1}{8}\Big(\frac{2}{x}+1\Big)^{4}$$
The derivative of function $y$ is: $$y'=\Big[(5-2x)^{-3}\Big]'+\frac{1}{8}\Bigg[\Big(\frac{2}{x}+1\Big)^{4}\Bigg]'$$
$$y'=-3(5-2x)^{-4}(5-2x)'+\frac{1}{8}\Bigg[4\Big(\frac{2}{x}+1\Big)^3\Big(\frac{2}{x}+1\Big)'\Bigg]$$
$$y'=-3(5-2x)^{-4}(-2)+\frac{1}{8}\Bigg[4\Big(\frac{2}{x}+1\Big)^3\Big(\frac{-2(x)'}{x^2}+0\Big)\Bigg]$$
$$y'=6(5-2x)^{-4}+\frac{1}{8}\Bigg[4\Big(\frac{2}{x}+1\Big)^3\Big(-\frac{2}{x^2}\Big)\Bigg]$$
$$y'=6(5-2x)^{-4}-\frac{8}{8}\Bigg[\Big(\frac{2}{x}+1\Big)^3\Big(\frac{1}{x^2}\Big)\Bigg]$$
$$y'=6(5-2x)^{-4}-x^{-2}\Big(\frac{2}{x}+1\Big)^3$$
