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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{- 2}, g = e^{x}

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

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

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

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

Simplify

(- \frac{2}{x ^{3}}) e^{x} + e^{x} x^{- 2} : - \frac{2 e ^{x}}{x ^{3}} + \frac{e ^{x}}{x ^{2}}

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

x^{2} - 4 x - 6, - x^{2} + 4 x + 4

\frac{d y}{d x} = y^{2} \cdot x^{- 3}

\frac{\partial}{\partial y} (\frac{4}{y ^{2}} + x)

\int 9 x e^{- 4 x} d x

\frac{d}{d x} (lo g_{x} (x))

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