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

The derivative of 2/(1-x^3) is (6x^2)/((1-x^3)^2)

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

The first derivative of 2/(1-x^3) is (6x^2)/((1-x^3)^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= 2 \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}

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

Simplify

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

= \frac{6 x ^{2}}{( 1 - x ^{3} ) ^{2}}

What is the derivative of 2/(1-x^3) ?
The derivative of 2/(1-x^3) is (6x^2)/((1-x^3)^2)
What is the first derivative of 2/(1-x^3) ?
The first derivative of 2/(1-x^3) is (6x^2)/((1-x^3)^2)