I am taking a course on deep learning and I a have a good understanding of High School math.
In the course they gave a formula saying that the derivative of a function $f(x)$

$f'(x) = \frac\lim{h\to0}\frac {f(x+h)-f(x)}{h} $ (formula 1) 

Which is the first principle of derivatives

Then they gave another formula saying that in numerical approximation the first principle don't work well, The formula was
$f'(x)=\frac\lim{h\to0} \frac{f(x+h)-f(x-h)}{2h}$ (formula 2)

They also said that the order of error in the first method is of $h$ and for the second is $h^2$

Which is much better assuming h is less than one.

I don't understand how this works because take $f(x)=x^3$ the triangle considered when we take $(x,f(x))$ and $(x+h,f(x+h))$ will be smaller than the triangle considered when taking $(x-h,f(x-h))$ and $(x+h,f(x+h))$ so shouldn't formula 1 give a better approximation of slope than the second. Since bigger triangles tend to make more errors?