What is (\partial)/(\partial x)(t^{-3}(x^2)/(2t)) ?

The answer to (\partial)/(\partial x)(t^{-3}(x^2)/(2t)) is x/(t^4)

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(\partial)/(\partial x)(t^{-3}(x^2)/(2t))

\frac{\partial}{\partial x} (t^{- 3} \frac{x ^{2}}{2 t})

\frac{x}{t ^{4}}

Solution steps

\frac{\partial}{\partial x} (t^{- 3} \frac{x ^{2}}{2 t})

Treat

t

as a constant

Take the constant out:

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

= t^{- 3} \frac{1}{2 t} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

= t^{- 3} \frac{1}{2 t} \cdot 2 x^{2 - 1}

Simplify

t^{- 3} \frac{1}{2 t} \cdot 2 x^{2 - 1} : \frac{x}{t ^{4}}

= \frac{x}{t ^{4}}

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What is (\partial)/(\partial x)(t^{-3}(x^2)/(2t)) ?
The answer to (\partial)/(\partial x)(t^{-3}(x^2)/(2t)) is x/(t^4)