What is (\partial)/(\partial x)(1/(1-x^4)) ?

The answer to (\partial)/(\partial x)(1/(1-x^4)) is (4x^3)/((1-x^4)^2)

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(\partial)/(\partial x)(1/(1-x^4))

\frac{\partial}{\partial x} (\frac{1}{1 - x ^{4}})

\frac{4 x ^{3}}{( 1 - x ^{4} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{1 - x ^{4}})

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((1 - x^{4})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 - x ^{4} ) ^{2}} \frac{\partial}{\partial x} (1 - x^{4})

= - \frac{1}{( 1 - x ^{4} ) ^{2}} \frac{\partial}{\partial x} (1 - x^{4})

\frac{\partial}{\partial x} (1 - x^{4}) = - 4 x^{3}

= - \frac{1}{( 1 - x ^{4} ) ^{2}} (- 4 x^{3})

Simplify

- \frac{1}{( 1 - x ^{4} ) ^{2}} (- 4 x^{3}) : \frac{4 x ^{3}}{( 1 - x ^{4} ) ^{2}}

= \frac{4 x ^{3}}{( 1 - x ^{4} ) ^{2}}

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What is (\partial)/(\partial x)(1/(1-x^4)) ?
The answer to (\partial)/(\partial x)(1/(1-x^4)) is (4x^3)/((1-x^4)^2)