What is the d/(dt)(1/(1-t)) ?

The d/(dt)(1/(1-t)) is 1/((1-t)^2)

What is the first d/(dt)(1/(1-t)) ?

The first d/(dt)(1/(1-t)) is 1/((1-t)^2)

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\frac{d}{d t} (\frac{1}{1 - t})

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

Solution steps

\frac{d}{d t} (\frac{1}{1 - t})

Apply exponent rule:

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

= \frac{d}{d t} ((1 - t)^{- 1})

Apply the chain rule:

- \frac{1}{( 1 - t ) ^{2}} \frac{d}{d t} (1 - t)

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

\frac{d}{d t} (1 - t) = - 1

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

Simplify

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

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