What is the derivative of (1/x)^3 ?

The derivative of (1/x)^3 is -3/(x^4)

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

The first derivative of (1/x)^3 is -3/(x^4)

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derivative of

(\frac{1}{x})^{3}

- \frac{3}{x ^{4}}

Solution steps

\frac{d}{d x} ((\frac{1}{x})^{3})

Apply the chain rule:

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

= 3 (\frac{1}{x})^{2} \frac{d}{d x} (\frac{1}{x})

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

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

Simplify

3 (\frac{1}{x})^{2} (- \frac{1}{x ^{2}}) : - \frac{3}{x ^{4}}

= - \frac{3}{x ^{4}}

What is the derivative of (1/x)^3 ?
The derivative of (1/x)^3 is -3/(x^4)
What is the first derivative of (1/x)^3 ?
The first derivative of (1/x)^3 is -3/(x^4)