What is the derivative of x^3e^{-3/x} ?

The derivative of x^3e^{-3/x} is 3e^{-3/x}x^2+3e^{-3/x}x

What is the first derivative of x^3e^{-3/x} ?

The first derivative of x^3e^{-3/x} is 3e^{-3/x}x^2+3e^{-3/x}x

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

3 e^{- \frac{3}{x}} x^{2} + 3 e^{- \frac{3}{x}} x

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = e^{- \frac{3}{x}}

= \frac{d}{d x} (x^{3}) e^{- \frac{3}{x}} + \frac{d}{d x} (e^{- \frac{3}{x}}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (e^{- \frac{3}{x}}) = \frac{3 e ^{- \frac{3}{x}}}{x ^{2}}

= 3 x^{2} e^{- \frac{3}{x}} + \frac{3 e ^{- \frac{3}{x}}}{x ^{2}} x^{3}

\frac{3 e ^{- \frac{3}{x}}}{x ^{2}} x^{3} = 3 e^{- \frac{3}{x}} x

= 3 e^{- \frac{3}{x}} x^{2} + 3 e^{- \frac{3}{x}} x

n = 1 \sum \infty \frac{7 n}{5 n + 1}

\int 20 x sec^{2} (x) d x

\frac{\partial}{\partial y} (\frac{x ^{2}}{1 + y ^{2}})

\frac{d}{d x} (- \frac{a}{x} + \frac{b}{x ^{2}})

- sin (2 x)

What is the derivative of x^3e^{-3/x} ?
The derivative of x^3e^{-3/x} is 3e^{-3/x}x^2+3e^{-3/x}x
What is the first derivative of x^3e^{-3/x} ?
The first derivative of x^3e^{-3/x} is 3e^{-3/x}x^2+3e^{-3/x}x