Proof of x² = 2x

$$ \begin{flalign} &\frac{d}{dx}(x^2) = 2 \ \ &f(x) = x^2 \ \ &f'(x) = \lim_{x \to 0} \frac{f(x+h) - f(x)}{h} \ \ &\text{So what is }f(x+h)?\ &\text{We just replace the x in the base formula with }(x+h)\ \\ &f(x+h) = (x+h)^2\ \ &f'(x) = \lim_{x \to 0} \frac{(x+h)^2-x^2}{h} \ &f'(x) = \lim_{x \to 0} \frac{x^2+2xh+h^2-x^2}{h} \ &f'(x) = \lim_{x \to 0} \frac{2xh+h^2}{h} \ &f'(x) = \lim_{x \to 0} \frac{h(2x+h)}{h} \ &f'(x) = \lim_{x \to 0} 2x+h \ \end{flalign} $$

left=-2; right=2;
bottom=-2; top=2;
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y=x^2
y=2x