Question

What is the derivative of `x*sqrt(4-x)`?

Answer 1

The answer is `=(8-3x)/(2sqrt(4-x))`

Explanation:

Use `(uv)'=u'v+uv'`
`u=x` `=>` `u'=1`
`v=sqrt(4-x)` `=>` `v'=1/(2sqrt(4-x))*-1`

`(x*sqrt(4-x))'=1*sqrt(4-x)-x/(2sqrt(4-x))`
`=(2(4-x)-x)/(2sqrt(4-x))=(8-2x-x)/(2sqrt(4-x))=(8-3x)/(2sqrt(4-x))`