What is (\partial)/(\partial t)(t^6e^{-x}) ?

The answer to (\partial)/(\partial t)(t^6e^{-x}) is 6e^{-x}t^5

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(\partial)/(\partial t)(t^6e^{-x})

\frac{\partial}{\partial t} (t^{6} e^{- x})

6 e^{- x} t^{5}

Solution steps

\frac{\partial}{\partial t} (t^{6} e^{- x})

Treat

x

as a constant

Take the constant out:

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

= e^{- x} \frac{\partial}{\partial t} (t^{6})

Apply the Power Rule:

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

= e^{- x} \cdot 6 t^{6 - 1}

Simplify

= 6 e^{- x} t^{5}

\int x^{2} cos (a x) d x

y^{^{'}} \cdot cos (t) + y \cdot sin (t) = tan (t)

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

\frac{d}{d x} (\frac{4}{( x + 3 ) ^{2}})

\frac{\partial}{\partial x} (2 - x^{2} + y^{2})

What is (\partial)/(\partial t)(t^6e^{-x}) ?
The answer to (\partial)/(\partial t)(t^6e^{-x}) is 6e^{-x}t^5