What is the derivative of x*e^{-x} ?

The derivative of x*e^{-x} is e^{-x}-e^{-x}x

What is the first derivative of x*e^{-x} ?

The first derivative of x*e^{-x} is e^{-x}-e^{-x}x

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derivative of

x \cdot e^{- x}

e^{- x} - e^{- x} x

Solution steps

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

Apply the Product Rule:

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

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

= \frac{d x}{d x} e^{- x} + \frac{d}{d x} (e^{- x}) x

\frac{d x}{d x} = 1

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

= 1 \cdot e^{- x} + (- e^{- x}) x

Simplify

= e^{- x} - e^{- x} x

\int 35 x^{4} d x

\frac{d}{d x} (\frac{3 + x}{1 - 3 x})

y = \frac{4 x}{1 + x ^{2}}, y = \frac{4 x ^{2}}{1 + x ^{3}}

\frac{\partial}{\partial x} (4 a x^{4} + 7 b (x, t) t^{3})

y = \frac{4 + x f ( x )}{x}

What is the derivative of x*e^{-x} ?
The derivative of x*e^{-x} is e^{-x}-e^{-x}x
What is the first derivative of x*e^{-x} ?
The first derivative of x*e^{-x} is e^{-x}-e^{-x}x