What is the derivative of (2/(x^3)^2) ?

The derivative of (2/(x^3)^2) is -(24)/(x^7)

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

The first derivative of (2/(x^3)^2) is -(24)/(x^7)

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

- \frac{24}{x ^{7}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

= 2 \cdot \frac{2}{x ^{3}} (- \frac{6}{x ^{4}})

Simplify

2 \cdot \frac{2}{x ^{3}} (- \frac{6}{x ^{4}}) : - \frac{24}{x ^{7}}

= - \frac{24}{x ^{7}}

What is the derivative of (2/(x^3)^2) ?
The derivative of (2/(x^3)^2) is -(24)/(x^7)
What is the first derivative of (2/(x^3)^2) ?
The first derivative of (2/(x^3)^2) is -(24)/(x^7)