How do you find the derivative of 5e^x sqrt(x)5exx?

1 Answer
Mar 10, 2015

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.