What is the (x^4e^{-x})^' ?

The (x^4e^{-x})^' is 4e^{-x}x^3-e^{-x}x^4

What is the first (x^4e^{-x})^' ?

The first (x^4e^{-x})^' is 4e^{-x}x^3-e^{-x}x^4

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(x^{4} e^{- x})^{^{'}}

4 e^{- x} x^{3} - e^{- x} x^{4}

Solution steps

(x^{4} e^{- x})^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{4}, g = e^{- x}

= (x^{4})^{^{'}} e^{- x} + (e^{- x})^{^{'}} x^{4}

(x^{4})^{'} = 4 x^{3}

(e^{- x})^{'} = - e^{- x}

= 4 x^{3} e^{- x} + (- e^{- x}) x^{4}

Simplify

= 4 e^{- x} x^{3} - e^{- x} x^{4}

\frac{\partial}{\partial x} (4 x - 3 x^{4} y^{2})

\int \frac{t ^{5}}{t ^{2} + 2} d t

\int \frac{1}{y ^{\frac{3}{2}}} d y

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

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

What is the (x^4e^{-x})^' ?
The (x^4e^{-x})^' is 4e^{-x}x^3-e^{-x}x^4
What is the first (x^4e^{-x})^' ?
The first (x^4e^{-x})^' is 4e^{-x}x^3-e^{-x}x^4