differentiate (1+2x^2)^(1/2)

This differentiation requires use of the chain rule. The first step is to differentiate the whole thing, treating the bracket as u, so u=1+2x². Therefore we are differentiating u^1/2. This means our first step gives us the value:   1/2*u^-1/2     (given student understands simple differentiation) Replacing u this gives us  1/2 *(1+2x²)^-1/2   but now we must multiply this by the differential of the inside of the bracket (u=1+2x²) differentiating gives:  du/dx=4x   as the constant term disappears. so putting this back in, you multiply our two answers together to give                          dy/dx = 1/2 *(1+2x²)^-1/2 *4x                            = 2x *(1+2x²)^-1/2   and so you have your answer.