Given that y = 2x² use differentiation from first principles to show that dy/dx = 4x - Edexcel - A-Level Maths Pure - Question 6 - 2022 - Paper 2

Now, we expand ( f(x+h) ):

$f(x+h) = 2(x+h)^2 = 2(x^2 + 2xh + h^2) = 2x^2 + 4xh + 2h^2$

Now we can substitute this back into the derivative formula.

Substituting into the limit:

$\frac{dy}{dx} = \lim_{h \to 0} \frac{(2x^2 + 4xh + 2h^2) - 2x^2}{h}$

This simplifies to:

$\frac{dy}{dx} = \lim_{h \to 0} \frac{4xh + 2h^2}{h}$

Which reduces to:

$\frac{dy}{dx} = \lim_{h \to 0} (4x + 2h)$

Taking the limit as ( h \to 0 ):

$\frac{dy}{dx} = 4x$