Calculus • Step-by-Step

Derivative of 1/x² with Steps

Find the derivative of 1/x² step by step. Rewrite as x^(-2) and apply the power rule to obtain -2/x³.

Problem Statement
ddx[1x2]\frac{d}{dx}[\frac{1}{x^2}]
Final Result
f′(x)=−2x3f'(x) = -\frac{2}{x^{3}}

Formula Required: Power Rule with Negative Powers

Bring down -2 and subtract 1 to get exponent -3.

ddx[x−2]=−2x−3=−2x3\frac{d}{dx}[x^{-2}] = -2x^{-3} = -\frac{2}{x^3}

Step-by-Step Solution

2 Steps
1

Set up the differentiation problem with respect to variable $x$.

ddx[1x2]\frac{d}{dx} \left[ \frac{1}{x^{2}} \right]
2

Apply the Power Rule to compute the derivative.

ddx[1x2]=−2x3\frac{d}{dx} \left[ \frac{1}{x^{2}} \right] = -\frac{2}{x^{3}}

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Common Questions About Derivative of 1/x²

How do you differentiate 1/x²?

Write 1/x² as x^(-2). Apply power rule: -2 · x^(-2 - 1) = -2x^(-3) = -2/x³.

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