A-Level Differentiation Part 2

Stuck again.

Question:
The maximum point on the curve with the equation y=xsin^0.5x where 0<x<pi is A. Show that the x coordinate of A satisfies the equation 2tanx+x=0.


I've differentiated it to sin^0.5x +xcosx/2sin^0.5x, but cant work out how to get the maximum point.

set **sin^0.5x +xcosx/2sin^0.5x to zero

multiply each term by *sin^0.5x

to get tanx you need to think of sinx/cosx ....*

If I times both sides by sin^0.5x then I get sinx+xcosx/2=0

What do I do from there?

you need to somehow get tanx to appear.... *

sinx+xcosx/2=0

2sinx+xcosx=0

2sinx/cosx+xcosx/cosx=0

=2tanx+x=0

Ok so I've done that, but how do I work out the x coordinate of A.

You don't have to. It simply asks you to show that it satisfies that equation and you've done it. It's a transcendental equation anyhow so you cannot solve it using analytical methods, unless you say x=0 but that's not the only solution.