How do you find the derivative of $2 e^{\sqrt{x}}$ $2e^(sqrtx)$ ?

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Answer 1 · 2016-06-26T06:27:27

$= \frac{e^{\sqrt{x}}}{\sqrt{x}}$ $= e^(sqrtx) /(sqrtx)$

using the chain rule you know that $(alpha e^{f(x)} )'= alpha f'(x) e^{f(x)}$

or you can see for yourself by noting that if

$y = alpha e^{f(x)}$

then

$y/alpha = e^{f(x)}$

and

$ln(y/alpha) = f(x)$

so $(ln(y/alpha))' = f'(x)$

ie $1/ (y/alpha) (1/alpha) y' = f'(x)$

so $y' = (y f'(x) ) = alpha f'(x) e^{f(x)}$

here that means that

$(2e^(sqrtx))' = 2e^(sqrtx) * (sqrtx)'$

$= 2e^(sqrtx) * 1/2 1/(sqrtx)$

$= e^(sqrtx) /(sqrtx)$

How do you find the derivative of 2e^(sqrtx)2e√x2e^(sqrtx)?