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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

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