= Numerical differentiation
{title2=$f'(x)\approx\dfrac{f(x+h)-f(x)}h$}
<Numerical differentiation> estimates <derivatives> from finitely many <function> values, often by differentiating an <interpolation polynomial> or using a <finite difference>. Its error combines <truncation error> from the formula with errors already present in the sampled values and additional <roundoff error>. Decreasing the sample spacing can decrease <truncation error> while increasing the effect of uncertain values. This tradeoff is explained by the <ill-posedness of numerical differentiation> when only an absolute value-error bound is available.
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