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    %% Differentiate Quotient of Polynomials
% Create two vectors to represent the polynomials in the quotient,
%
% $$\frac{x^4-3x^2-1}{x+4}.$$
%
p = [1 0 -3 0 -1];
v = [1 4];

%%
% Use |polyder| with two output arguments to calculate
%
% $$\frac{q(x)}{d(x)}=\frac{d}{dx} \left[ \frac{p(x)}{v(x)} \right].$$
%
[q,d] = polyder(p,v)

%%
% The result is 
%
% $$\frac{q(x)}{d(x)}=\frac{3x^4+16x^3-3x^2-24x+1}{x^2+8x+16}.$$
%