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?