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622ghernandezc

18.10.2020

Mathematics

$f(x)=x^2\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^2-x^2}{h}\\\\=\dfrac{x^2+2xh+h^2-x^2}{h}=\dfrac{2xh+h^2}{h}\\\\=\dfrac{h(2x+h)}{h}=\boxed{2x+h}$

Used:
(a + b)² = a² + 2ab + b²

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