What is (\partial)/(\partial t)(t^8e^{-x}) ?

The answer to (\partial)/(\partial t)(t^8e^{-x}) is 8e^{-x}t^7

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(\partial)/(\partial t)(t^8e^{-x})

\frac{\partial}{\partial t} (t^{8} e^{- x})

8 e^{- x} t^{7}

Solution steps

\frac{\partial}{\partial t} (t^{8} e^{- x})

Treat

x

as a constant

Take the constant out:

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

= e^{- x} \frac{\partial}{\partial t} (t^{8})

Apply the Power Rule:

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

= e^{- x} \cdot 8 t^{8 - 1}

Simplify

= 8 e^{- x} t^{7}

e^{x} (2 x + 2)

\int_{0}^{16} 8 x d x

k = 1 \sum \infty \frac{1}{1 + k ^{2}}

f (x) = x^{5} - 2 x^{3} + x - 1

\frac{d}{d x} (\frac{6 x + 2 x ^{2}}{( 3 + 2 x ) ^{2}})

What is (\partial)/(\partial t)(t^8e^{-x}) ?
The answer to (\partial)/(\partial t)(t^8e^{-x}) is 8e^{-x}t^7