What is (\partial)/(\partial x)(2/(1-3x^3)) ?

The answer to (\partial)/(\partial x)(2/(1-3x^3)) is (18x^2)/((1-3x^3)^2)

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(\partial)/(\partial x)(2/(1-3x^3))

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

\frac{18 x ^{2}}{( 1 - 3 x ^{3} ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (1 - 3 x^{3}) = - 9 x^{2}

= 2 (- \frac{1}{( 1 - 3 x ^{3} ) ^{2}} (- 9 x^{2}))

Simplify

2 (- \frac{1}{( 1 - 3 x ^{3} ) ^{2}} (- 9 x^{2})) : \frac{18 x ^{2}}{( 1 - 3 x ^{3} ) ^{2}}

= \frac{18 x ^{2}}{( 1 - 3 x ^{3} ) ^{2}}

What is (\partial)/(\partial x)(2/(1-3x^3)) ?
The answer to (\partial)/(\partial x)(2/(1-3x^3)) is (18x^2)/((1-3x^3)^2)