Find the given higher-order derivative.f''(x) = 9- 3/xf'''(x)=

Answer:[tex]f'''(x)=\frac{3}{x^{2}}[/tex]Step-by-step explanation:We are given with Second-order derivative of function f(x).[tex]f''(x)=9-\frac{3}{x}[/tex]We need to find Third-order derivative of the function f(x).[tex]f''(x)=9-\frac{3}{x}=9-3x^{-1}[/tex]We know that,f'''(x) = (f''(x))'So,[tex]f'''(x)=\frac{\mathrm{d}\,f''(x)}{\mathrm{d} x}[/tex][tex]f'''(x)=\frac{\mathrm{d}\,(9-3x^{-1})}{\mathrm{d} x}[/tex][tex]f'''(x)=\frac{\mathrm{d}\,9}{\mathrm{d} x}-\frac{\mathrm{d}\,3x^{-1}}{\mathrm{d} x}[/tex][tex]f'''(x)=0-3\frac{\mathrm{d}\,x^{-1}}{\mathrm{d} x}[/tex][tex]f'''(x)=-3(-1)x^{-1-1}[/tex][tex]f'''(x)=3x^{-2}[/tex][tex]f'''(x)=\frac{3}{x^{2}}[/tex]Therefore, [tex]f'''(x)=\frac{3}{x^{2}}[/tex]