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

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

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

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

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

- e^{x^{2}} \cdot 2 x

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - e^{x^{2}} \cdot 2 x

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