Question

How can I solve it??ans= 1/2 -1/2x^2​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Differentiate using the power rule

$\frac{d}{dx}$(a$x^{n}$) = na$x^{n-1}$

Simplify the expression by dividing both terms on the numerator by 2x²

$\frac{x^3+x}{2x^2}$

= $\frac{x^3}{2x^2}$ + $\frac{x}{2x^2}$

= $\frac{1}{2}$ x + $\frac{1}{2}$ $x^{-1}$

Hence differentiating gives

$\frac{1}{2}$ - $\frac{1}{2}$$x^{-2}$

= $\frac{1}{2}$ - $\frac{1}{2x^2}$