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

\frac{1}{s ^{2} + s + 1} \cdot \frac{1}{s}

\frac{d}{d x} (1 - 5 x)

\frac{d ^{3}}{d x ^{3}} (\frac{1}{1 + x ^{2}})

\frac{d y}{d x} = \frac{1}{x ( ln ( 2 ) )}

f (x) = (\frac{b}{a + z ^{2}})^{7}

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