What is the derivative of xe^{-1/x} ?

The derivative of xe^{-1/x} is e^{-1/x}+(e^{-1/x})/x

What is the first derivative of xe^{-1/x} ?

The first derivative of xe^{-1/x} is e^{-1/x}+(e^{-1/x})/x

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derivative of

x e^{- \frac{1}{x}}

e^{- \frac{1}{x}} + \frac{e ^{- \frac{1}{x}}}{x}

Solution steps

\frac{d}{d x} (x e^{- \frac{1}{x}})

Apply the Product Rule:

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

f = x, g = e^{- \frac{1}{x}}

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

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

\frac{d}{d x} (e^{- \frac{1}{x}}) = \frac{e ^{- \frac{1}{x}}}{x ^{2}}

= 1 \cdot e^{- \frac{1}{x}} + \frac{e ^{- \frac{1}{x}}}{x ^{2}} x

Simplify

1 \cdot e^{- \frac{1}{x}} + \frac{e ^{- \frac{1}{x}}}{x ^{2}} x : e^{- \frac{1}{x}} + \frac{e ^{- \frac{1}{x}}}{x}

= e^{- \frac{1}{x}} + \frac{e ^{- \frac{1}{x}}}{x}

x (e^{\frac{y}{x}} - 1) \frac{d y}{d x} = e^{\frac{y}{x}} (y - x)

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{3}})

\int \frac{sin ( x )}{cos ( x ) - cos ^{2} ( x )} d x

\frac{d y}{d x} = \frac{( 1 - y )}{1 - x}

\int 4 cos (2 θ - 5) d θ

What is the derivative of xe^{-1/x} ?
The derivative of xe^{-1/x} is e^{-1/x}+(e^{-1/x})/x
What is the first derivative of xe^{-1/x} ?
The first derivative of xe^{-1/x} is e^{-1/x}+(e^{-1/x})/x