How do you find the derivative of $5 e^{x} \sqrt{x}$ $5e^x sqrt(x)$ ?

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Answer 1 · 2015-03-10T20:12:23

I would use the Product Rule where if you have:

$y = f (x) g (x)$ $y=f(x)g(x)$ then
$y'=f'(x)g(x)+f(x)g'(x)$

In your case you get:
$y'=5e^xsqrt(x)+5e^x1/(2sqrt(x))$
$=5e^x[sqrt(x)+1/(2sqrt(x))]=$
$=5e^x[(2x+1)/(2sqrt(x))]$

By the way:
It is a good idea, after you memorize the first derivative rules, to memorize: $d/(dx)(sqrtx)=1/(2sqrtx)$ .

The square root function comes up a lot, because it is the length of a diagonal (hypotenuse of a right triagle). So it is involved in distance.

How do you find the derivative of 5e^x sqrt(x)5ex√x5e^x sqrt(x)?