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

The derivative of 2/(x^3+2) is -(6x^2)/((x^3+2)^2)

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

The first derivative of 2/(x^3+2) is -(6x^2)/((x^3+2)^2)

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derivative of

\frac{2}{x ^{3} + 2}

- \frac{6 x ^{2}}{( x ^{3} + 2 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{1}{( x ^{3} + 2 ) ^{2}} \cdot 3 x^{2}) : - \frac{6 x ^{2}}{( x ^{3} + 2 ) ^{2}}

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

What is the derivative of 2/(x^3+2) ?
The derivative of 2/(x^3+2) is -(6x^2)/((x^3+2)^2)
What is the first derivative of 2/(x^3+2) ?
The first derivative of 2/(x^3+2) is -(6x^2)/((x^3+2)^2)