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

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

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

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

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

e^{\frac{x ^{2}}{2}} x

Solution steps

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

Apply the chain rule:

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

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

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

= e^{\frac{x ^{2}}{2}} x

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