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 u1/2. 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.
RS
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