Question

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

Answer 1

I would use the Product Rule where if you have:

`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.