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

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Answer 1 · 2016-02-22T00:49:46

Use the chain rule to find that

$d/dx e^(x^2/2) = xe^(x^2/2)$

The chain rule states that given two differentiable functions $f$ and $g$

$d/dxf@g(x) = f'(g(x))*g'(x)$

In this case, let $f(x) = e^x$ and $g(x) = 1/2x^2$

Then $f'(x) = e^x$ and $g'(x) = 1/2(2x) = x$

So, by the chain rule, we have

$d/dxe^(x^2/2) = d/dxf@g(x)$

$=f'(g(x))*g'(x)$

$=e^(g(x))*x$

$=xe^(x^2/2)$

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