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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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\frac{\partial}{\partial x} (8 x^{3} - 24 x y + y^{3})

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