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

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

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

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

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

- 2 e^{- x^{2}} x - 1

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d x}{d x} = 1

= - 2 e^{- x^{2}} x - 1

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