What is the d/(dt)(t^{-2}ln(t)) ?

The d/(dt)(t^{-2}ln(t)) is (-2ln(t)+1)/(t^3)

What is the first d/(dt)(t^{-2}ln(t)) ?

The first d/(dt)(t^{-2}ln(t)) is (-2ln(t)+1)/(t^3)

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

\frac{- 2 ln ( t ) + 1}{t ^{3}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{- 2}, g = ln (t)

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

\frac{d}{d t} (t^{- 2}) = - \frac{2}{t ^{3}}

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

= (- \frac{2}{t ^{3}}) ln (t) + \frac{1}{t} t^{- 2}

Simplify

(- \frac{2}{t ^{3}}) ln (t) + \frac{1}{t} t^{- 2} : \frac{- 2 ln ( t ) + 1}{t ^{3}}

= \frac{- 2 ln ( t ) + 1}{t ^{3}}

What is the d/(dt)(t^{-2}ln(t)) ?
The d/(dt)(t^{-2}ln(t)) is (-2ln(t)+1)/(t^3)
What is the first d/(dt)(t^{-2}ln(t)) ?
The first d/(dt)(t^{-2}ln(t)) is (-2ln(t)+1)/(t^3)