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

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

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d/(dt)(1/t)

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 1 \cdot t^{- 1 - 1}

Simplify

- 1 \cdot t^{- 1 - 1} : - \frac{1}{t ^{2}}

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

x \to 1 + lim (\frac{x + 2}{x + 1})

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(a + \frac{b}{x ^{2}})^{3}