Could someone please double check my workings.

I have this equation

Y=[4th root(x^2+4)]^3

Rearranged is [(x^2+4)^1/4]^3

When I apply the chain rule

Y=[(x^2+4)^1/4]^3

U=(x^2+4)^1/4 ..

u`=1/4(x^2+4)^-3/4.2x

Y=u^3 ..

Y`=3u^2

=u`.y` 3[1/4(x^2+4)^-3/4.2x]^2

= .. 3[1/2x(x^2+4)^-3/4]^2

= ... [3/2x(x^2+4)^-3/4]^2

= 3x/2(x^2+4)^(-3/4+2/4)]

= 3x/2(x^2+4)^-1/4

Solution is 3x/[2(x^2+4)^1/4]

Is my workings correct?