Differentiate y = √(1 + 3x²) with respect to x

To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In this example, if we let u = 1 + 3x², then we get y = √(u), which means when we differentiate with respect to u, dy/du = 1/(2√(u)). u = 1 + 3x² which means du/dx = 6x, so dy/dx = 6x/(2√(u)), or 3x/√(1 + 3x²). (This can also be expressed as 3x(1 + 3x²)^-0.5).