Question

‏ Derivative for 2/x is ?

Answer 1

`-2x^(-2) \ \text{or} \ -(2)/(x^2)`

Explanation:

Find
`(d)/(dx)[(2)/(x) ]`.

(1) - Pull out the constant

`(d)/(dx)[(2)/(x) ]\\\\\Longrightarrow 2(d)/(dx)[(1)/(x) ]`

(2) - Flip the fraction

`2(d)/(dx)[(1)/(x)]\\\\\Longrightarrow 2(d)/(dx)[x^(-1)]`

(3) - Apply the power rule]

`\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\(d)/(dx)[x^n]=nx^(n-1) \end{array}\right}\\\\\\2(d)/(dx)[x^(-1)]\\\\\Longrightarrow 2[(-1)x^(-1-1)]\\\\\Longrightarrow 2[-x^(-2)]\\\\\therefore \boxed{\boxed{(d)/(dx)[(2)/(x) ] =-2x^(-2) \ \text{or} \ -(2)/(x^2)}}`

Thus, the problem is solved.