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

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

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

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

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derivative of

(e^{- x})^{2}

- 2 e^{- 2 x}

Solution steps

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

Simplify

(e^{- x})^{2} : e^{- 2 x}

= \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}

lo g_{10} (1 - x)

e^{- 2} x

(2^{x})^{2}

lo g_{10} (1 + x)

sin^{2} (x^{2} + 1)

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