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}

\frac{d}{d x} (1 + 4 x^{\frac{3}{2}})

\int \frac{d ^{2} w}{2} d x

f (t) = ln (t + 1)

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

t \cdot \frac{d y}{d t} + 37 y = \frac{1}{t}

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