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Popular >

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

Solution

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

Solution

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}

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

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

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Frequently Asked Questions (FAQ)

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}