If y = 2(x^2+1)^3, what is dy/dx?

Since the equation for y is a composite function (applying one function to another function) we need to use the chain rule to answer this question. Firstly let u = x^2+1 . This allows us to write y = 2u^3. Differentiating y with respect to u gives us: dy/du = 6u^2. Next we differentiate our equation for u with respect to x, which gives us: du/dx = 2x Finally we use these two equations to obtain dy/dx by using the following formula: dy/dx = (dy/du)(du/dx) = (6u^2)(2x) = (6(x^2+1)^2)*(2x) = 12x(x^2+1)^2 Hence we have obtained dy/dx in terms of x and y.