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})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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}

d er i v a t i v e lo g_{10} (x - 1)

\frac{d}{d s} (3 s^{2})

d er i v a t i v e y = \frac{( x ^{5} + x ^{2} )}{( x ^{3} + 1 )}

\frac{d}{d t} (65 + 2 t - 3 t^{2})

d er i v a t i v e - 2 ln (x)

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}