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

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

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

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

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

e^{2 x} \cdot 2

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= e^{2 x} \cdot 2

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