Differentiate y = (x^2 + 1)^1/3

Use the chain rule to do this. First set u= x^2 + 1. We chose u to be this because u^1/3 is much simpler to differentiate. Then find du/dx = 2x. Now find dy/du = 1/3 * u^-2/3 = 1/3 * (x² +1)^-2/3. Now by the chain rule, dy/dx = dy/du * du/dx. Therefore dy/ dx = 2x * (1/3 * (x² +1)^-2/3 )= 2x/3 * (x²+1)^-2/3