Given $$y=(x+1)\sqrt{x},\qquad x0,$$ find: $\frac{\mathrm{d}y}{\mathrm{d}x}$, expressed as a s

Question

Given $$y=(x+1)\sqrt{x},\qquad x>0,$$ find: $\frac{\mathrm{d}y}{\mathrm{d}x}$, expressed as a single fraction; the gradient when $x=1$.

Accepted Answer

$y'=\frac{(3x+1)}{(2\sqrt{x})}$; gradient $2$.

Differentiation