Question

What is the differentiation of x–²?

Answer 1

$\underline{ \large{ \text{Answer}}} : \\ \\ \text{let} \: \text{y} = { \text{x}}^{ - 2} \\ \\ \text{Differentiating both sides w. r. to x, we get} \\ \\ \frac{ \text{dy}}{ \text{dx}} = \frac{ \text{d}}{ \text{dx}} ( { \text{x}}^{ - 2} ) \\ \\ = ( - 2) \: { \text{x}}^{ (- 2 - 1)} \\ \\ = ( - 2) \: { \text{x}}^{ - 3} \\ \\ \implies\boxed{\frac{ \text{dy}}{ \text{dx}} = ( - 2) \: { \text{x}}^{ - 3}}$

$\begin{bmatrix} \text{RULE : } \\ \\ \frac{ \text{d}}{ \text{dx}} ( { \text{x}}^{ \text{n}}) = \text{n} \: { \text{x}}^{ \text{n - 1}} \end{bmatrix}$

$\bigstar \: \underline{ \large{ \text{MarkAsBrainliest}}} \: \bigstar$