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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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