Differentiate the equation y = (1+x^2)^3 with respect to (w.r.t.) x using the chain rule. (Find dy/dx)

For this example it would be better to use a dummy variable (a variable just to help with solving the equation but isn't a part of the final answer). Let us say our dummy variable, t = 1+x^2. So, substituting t into the equation, we now have y = t^3. Let us differentiate y w.r.t. t, dy/dt = 3t^2 and let us differentiate t w.r.t. x, dt/dx = 2x. So now, we have two new equations, dy/dt and dt/dx. If we multiply these two together using the chain rule - dy/dt * dt/dx = dy/dx (which is what we are trying to find), we end up with dy/dx = 3t^2 * 2x. Substitute x back into the equation dy/dx = 3(1+x^2)^2 * 2x = 6x(1+x^2)^2. (FINAL ANSWER)