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

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

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d/(dt)(t-1/t)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d t}{d t} = 1

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

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

Simplify

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

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