Question

Differentiate the function h(x) using the quotient rule. h(x) =2x+5 /2--x

Answer 1

$h'(x)=\frac{\frac{d}{dx}[2x+5] (2-x)-\frac{d}{dx}[2-x](2x+5) }{(2-x)^2}\\=\frac{2(2-x)-(-1)(2x+5)}{(2-x)^2} \\=\frac{4-2x+2x+5}{(2-x)^2}\\=\frac{9}{(2-x)^2} \\=\frac{9}{x^2-4x+4}$