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

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} y^{0}

\frac{d ^{2}}{d x ^{2}} (e^{3 x} cos (2 x))

\frac{d}{d x} (9 sin (x) cos (x))

in v erse l a pl a ce \frac{1}{s ^{2} + 2 ^{2}}

\frac{d x}{d t} = - \frac{5 x}{100}

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