What is the derivative of x^2e^{1/x} ?

The derivative of x^2e^{1/x} is 2e^{1/x}x-e^{1/x}

What is the first derivative of x^2e^{1/x} ?

The first derivative of x^2e^{1/x} is 2e^{1/x}x-e^{1/x}

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derivative of

x^{2} e^{\frac{1}{x}}

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = e^{\frac{1}{x}}

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

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

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

\frac{\partial}{\partial x} (t^{2} x - t)

\int \frac{x ^{2}}{x ^{4} - 20 x ^{2} - 125} d x

\frac{d}{d x} (5 \cdot 4^{x})

\frac{d}{d x} (lo g_{4} (x) (2^{3 x} + e^{x^{4}})^{- 2})

\int e^{(a - b) x} d x

What is the derivative of x^2e^{1/x} ?
The derivative of x^2e^{1/x} is 2e^{1/x}x-e^{1/x}
What is the first derivative of x^2e^{1/x} ?
The first derivative of x^2e^{1/x} is 2e^{1/x}x-e^{1/x}