Question

For the following voltage function, find the numerical differentiation of first order using the finite divided-difference formula at a point, 1, - 4.5 s with step forward, backward and center finite divide-difference formula at a point t1=4.5 s with step size, h=0.i s, where i=72

v(t) = 20sint-t^3/18

Evaluate the values using the conventional differentiation formula aiso and hence comment which numerical method produce better result based on the percentage of true error.

Answer 1

\frac{d}{dt}\left(20\sin \left(t\right)-\frac{t^3}{18}\right)\\ \mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\ =\frac{d}{dt}\left(20\sin \left(t\right)\right)-\frac{d}{dt}\left(\frac{t^3}{18}\right)\\ =20\cos \left(t\right)\\ =20\cos \left(t\right)-\frac{t^2}{6}