What is the derivative of e^{1/2 x^2} ?

The derivative of e^{1/2 x^2} is e^{(x^2)/2}x

What is the first derivative of e^{1/2 x^2} ?

The first derivative of e^{1/2 x^2} is e^{(x^2)/2}x

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\frac{d}{d x} (e^{\frac{1}{2} x^{2}})

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

Solution steps

\frac{d}{d x} (e^{\frac{1}{2} x^{2}})

Simplify

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

= \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

\frac{d}{d x} (2^{3 x + 1} ln (5 x - 11))

e^{\frac{t}{2}} \cdot cos (2 t)

\int 9 sin (ln (x)) d x

\int 2 x e^{2 y} d y

\int (x + 18) 36 x + x^{2} d x

What is the derivative of e^{1/2 x^2} ?
The derivative of e^{1/2 x^2} is e^{(x^2)/2}x
What is the first derivative of e^{1/2 x^2} ?
The first derivative of e^{1/2 x^2} is e^{(x^2)/2}x