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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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