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

The derivative of e^{(x/2 ^2}) is (e^{(x^2)/4}x)/(2)

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

The first derivative of e^{(x/2 ^2}) is (e^{(x^2)/4}x)/(2)

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

\frac{e ^{\frac{x ^{2}}{4}} x}{2}

Solution steps

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

Simplify

e^{(\frac{x}{2})^{2}} : e^{\frac{x ^{2}}{4}}

= \frac{d}{d x} (e^{\frac{x ^{2}}{4}})

Apply the chain rule:

e^{\frac{x ^{2}}{4}} \frac{d}{d x} (\frac{x ^{2}}{4})

= e^{\frac{x ^{2}}{4}} \frac{d}{d x} (\frac{x ^{2}}{4})

\frac{d}{d x} (\frac{x ^{2}}{4}) = \frac{x}{2}

= e^{\frac{x ^{2}}{4}} \frac{x}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{\frac{x ^{2}}{4}} x}{2}

What is the derivative of e^{(x/2 ^2}) ?
The derivative of e^{(x/2 ^2}) is (e^{(x^2)/4}x)/(2)
What is the first derivative of e^{(x/2 ^2}) ?
The first derivative of e^{(x/2 ^2}) is (e^{(x^2)/4}x)/(2)