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}}

x d x - y^{2} d y = 0

y^{^{''}} + (- 2 a) y^{^{'}} + (a^{2}) y = 0

x \to 5 - lim (\frac{3}{5 - x})

\frac{\partial}{\partial y} (y + y ln (x y))

\int_{0}^{2} t^{3} (1 + t^{4})^{3} d t

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