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

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

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

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

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

e^{x^{2}} x

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \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

= \frac{1}{2} e^{x^{2}} \cdot 2 x

Simplify

\frac{1}{2} e^{x^{2}} \cdot 2 x : e^{x^{2}} x

= e^{x^{2}} x

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