(dy/dx)=X^3/8 - 1/2x^3.

Question

what is sqrt( 1+(dy/dx)^2 ) and that multiplied by (dy/dx)

Answer 1

It is sqrt(dy/dx^2 + dy/dx^4)

Is your first dy/dx term x^(3/8) or (x^3)/8 ? Is the second term (1/2)x^2 or 1/(2x^3) ?

It seems to me all you have to do is substitute the dy/dx you already know into whatever you want to calculate.