What is the d/(dt)(1/(2*a*t^2)) ?

The d/(dt)(1/(2*a*t^2)) is -1/(at^3)

What is the first d/(dt)(1/(2*a*t^2)) ?

The first d/(dt)(1/(2*a*t^2)) is -1/(at^3)

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\frac{d}{d t} (\frac{1}{2 \cdot a \cdot t ^{2}})

- \frac{1}{a t ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{a t ^{3}}

What is the d/(dt)(1/(2*a*t^2)) ?
The d/(dt)(1/(2*a*t^2)) is -1/(at^3)
What is the first d/(dt)(1/(2*a*t^2)) ?
The first d/(dt)(1/(2*a*t^2)) is -1/(at^3)