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Popular >

derivative of 1/(x^3-3)

Solution

derivative of

\frac{1}{x ^{3} - 3}

Solution

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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