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

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

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

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

2 e^{- x} t

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= e^{- x} \cdot 2 t^{2 - 1}

Simplify

= 2 e^{- x} t

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