Given that y = (1 + 3x^2)^(1/3) , use the chain rule to find dy/dx in terms of x.
Take u = 1+3x2 , this gives that y = u1/3 . By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u1/3 with respect to u gives dy/du = (1/3)u-2/3. By differentiating u = 1 + 3x2 with respect to x gives du/dx = 6x. Using the formula highlighted gives the answer dy/dx = 2x(1+3x2)-2/3 which we have obtained by substituting u back in.
