Derivative Problem

Question

g(x)=(x^3+2)(sqaure root of x-1/x)

Answer 1

Write (x³ + 2)(x − x^-1)^0.5.

Take d[(x³ + 2)(x − x^-1)^0.5]/dx as (x³ + 2) times d(x − x^-1)^0.5/dx plus d(x³ + 2)/dx times (x − x^-1)^0.5.

Rewrite as (x³ + 2)(0.5)(1+x^-2)(x − x^-1)^-0.5 + (3x²)(x − x^-1)^0.5.

This can be condensed to 0.5(x³ + x + 2x^-2 + 2) ÷ (x − x^-1)^0.5 + 3x²(x − x^-1)^0.5.