What is the derivative of (1+x^3)^{-1} ?

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

What is the first derivative of (1+x^3)^{-1} ?

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

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derivative of

(1 + x^{3})^{- 1}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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