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

Question

13318 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-03T06:07:13

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

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

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

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