y= u+3/u-1 u=x^1/3 find dy/dx at x=8

Answer 1

dy/dx = dy/du du/dx

du/dx = (1/3)x^-(2/3)

dy/du = [(u-1)-(u+3)]/(u-1)^2
= [(x^(1/3)-1)-(x^(1/3)+3)/(x^(1/3)-1)^2
= -4 / (x^(2/3) -2x^(1/3)+1)

so
dy/du * du/dx
=(-4/3)(x^-(2/3)) /(x^(2/3) -2x^(1/3)+1)
= -4/3(x^4/3-2x +x^(2/3))

Answer 2

luckily 8^(1/3) = 2 :)