How do you differentiate $e^{\frac{1}{2 x}}$ $e^(1/(2x))$ ?

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Answer 1 · 2017-06-05T21:43:15

$- \frac{1}{2 x^{2}} (e^{\frac{1}{2 x}})$ $-1/(2x^2)(e^(1/(2x)))$

Using the chain rule,

$d/dx(e^f(g))=e^f(x)xxf'(x)$

So in this case, $f(x)=(2x)^(-1)$ .

The derivative of this function is

$f'(x)=-(2x)^-2xx2=-2/(2x)^2=-2/(4x^2)=-1/(2x^2)$

Therefore,

$d/dx(e^(1/(2x)))=e^(1/(2x))xx(-1/(2x^2))=-1/(2x^2)(e^(1/(2x)))$

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