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

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

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

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

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

- 2 e^{- 2 x}

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} (- 2)

Simplify

= - 2 e^{- 2 x}

s l o p e y = 6 x + x^{2}

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