What is the d/(dt)(5/(5-t)) ?

The d/(dt)(5/(5-t)) is 5/((5-t)^2)

What is the first d/(dt)(5/(5-t)) ?

The first d/(dt)(5/(5-t)) is 5/((5-t)^2)

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\frac{d}{d t} (\frac{5}{5 - t})

\frac{5}{( 5 - t ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{5}{5 - t})

Take the constant out:

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

= 5 \frac{d}{d t} (\frac{1}{5 - t})

Apply exponent rule:

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

= 5 \frac{d}{d t} ((5 - t)^{- 1})

Apply the chain rule:

- \frac{1}{( 5 - t ) ^{2}} \frac{d}{d t} (5 - t)

= - \frac{1}{( 5 - t ) ^{2}} \frac{d}{d t} (5 - t)

\frac{d}{d t} (5 - t) = - 1

= 5 (- \frac{1}{( 5 - t ) ^{2}} (- 1))

Simplify

5 (- \frac{1}{( 5 - t ) ^{2}} (- 1)) : \frac{5}{( 5 - t ) ^{2}}

= \frac{5}{( 5 - t ) ^{2}}