Answer:
see explanation
Step-by-step explanation:
Differentiate using the power rule
[tex]\frac{d}{dx}[/tex](a[tex]x^{n}[/tex]) = na[tex]x^{n-1}[/tex]
Simplify the expression by dividing both terms on the numerator by 2x²
[tex]\frac{x^3+x}{2x^2}[/tex]
= [tex]\frac{x^3}{2x^2}[/tex] + [tex]\frac{x}{2x^2}[/tex]
= [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{2}[/tex] [tex]x^{-1}[/tex]
Hence differentiating gives
[tex]\frac{1}{2}[/tex] - [tex]\frac{1}{2}[/tex][tex]x^{-2}[/tex]
= [tex]\frac{1}{2}[/tex] - [tex]\frac{1}{2x^2}[/tex]
