What is (\partial}{\partial x}(e^{\frac{x^2)/2}) ?

The answer to (\partial}{\partial x}(e^{\frac{x^2)/2}) is e^{(x^2)/2}x

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(\partial}{\partial x}(e^{\frac{x^2)/2})

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

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

Solution steps

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

Apply the chain rule:

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

= e^{\frac{x ^{2}}{2}} \frac{\partial}{\partial x} (\frac{x ^{2}}{2})

\frac{\partial}{\partial x} (\frac{x ^{2}}{2}) = x

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

f (x) = \frac{- 8 x}{x ^{2} + 1}, (1, - 4)

y^{^{''}} + 3.26 y^{^{'}} + 2.66 y = 0

\frac{\partial}{\partial x} (e^{x} (x + 2 y))

\frac{\partial}{\partial y} (x^{2} - 6 y)

y^{^{''}} + 14 y^{^{'}} + 49 y = 0, y (1) = 0, y^{^{'}} (1) = 1

What is (\partial}{\partial x}(e^{\frac{x^2)/2}) ?
The answer to (\partial}{\partial x}(e^{\frac{x^2)/2}) is e^{(x^2)/2}x