Calculators and numerical differentiation

[Wes Loewer]

(11-03-2020 10:14 PM)Albert Chan Wrote:  Slightly off topics, for f(x) = x*g(x), getting f'(0) is easier taking limit directly.

\(f(x) = x·g(x) = x·\sqrt[3]{x^2+x}\)

\(f'(0) = \displaystyle{\lim_{h \to 0}} {f(h)-f(0)\over h}
= \displaystyle{\lim_{h \to 0}}\; g(h) = g(0) = 0\)

If you pull out an \(x\), then \( x \cdot (x^2+x)^{1/3}\) becomes \( x^{4/3} \cdot (x+1)^{1/3}\) which the non-CAS Npsire handles correctly.