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

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

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

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

- e^{- x} t^{2}

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x) = - 1

= t^{2} e^{- x} (- 1)

Simplify

= - e^{- x} t^{2}

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