What is the derivative of (1/x ^2) ?

The derivative of (1/x ^2) is -2/(x^3)

What is the first derivative of (1/x ^2) ?

The first derivative of (1/x ^2) is -2/(x^3)

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\frac{d}{d x} ((\frac{1}{x})^{2})

- \frac{2}{x ^{3}}

Solution steps

\frac{d}{d x} ((\frac{1}{x})^{2})

Apply the chain rule:

2 \cdot \frac{1}{x} \frac{d}{d x} (\frac{1}{x})

= 2 \cdot \frac{1}{x} \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= 2 \cdot \frac{1}{x} (- \frac{1}{x ^{2}})

Simplify

2 \cdot \frac{1}{x} (- \frac{1}{x ^{2}}) : - \frac{2}{x ^{3}}

= - \frac{2}{x ^{3}}

\frac{d}{d x} (- 2 x^{2} + 4 x - 4)

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\frac{\partial}{\partial y} (3.5 x y cos (x yz))

\int \frac{1}{9 x ^{2} - 1} d x

What is the derivative of (1/x ^2) ?
The derivative of (1/x ^2) is -2/(x^3)
What is the first derivative of (1/x ^2) ?
The first derivative of (1/x ^2) is -2/(x^3)