Problem 42588. Derivative function

Solution 773931

Submitted on 8 Nov 2015 by Alberto Comin

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Test	Status	Code Input and Output
1	Pass	%% f = @sin; df = Derivative(f); x = 10*rand(10000,1); dy = cos(x); assert(max(abs((dy-df(x))./dy))<1e-13)
2	Pass	%% f = @log; df = Derivative(f); x = exp(500*rand(10000,1)); dy = 1./x; assert(max(abs((dy-df(x))./dy))<1e-13)
3	Pass	%% f = @exp; df = Derivative(f); x = 50*(rand(10000,1)-0.5); dy = exp(x); assert(max(abs((dy-df(x))./dy))<1e-13)
4	Pass	%% t = 10rand; f = @(x)1./(x+t); df = Derivative(f); x = 100(rand(10000,1)-0.5); x(x==-t) = 1; dy = -1./(x+t).^2; assert(max(abs((dy-df(x))./dy))<1e-13)
5	Pass	%% t = 10rand-5; f = @(x)atan(tx); df = Derivative(f); x = 100(rand(10000,1)-0.5); dy = t./(t^2x.^2 + 1); assert(max(abs((dy-df(x))./dy))<1e-13)
6	Pass	%% for t = 2:6 f = @(x)t.^x./(sin(x).^t+cos(x).^t); df = Derivative(f); x = 3+rand(10000,1); dy = (t.^x.log(t))./(cos(x).^t+sin(x).^t)-... (t.^x.(t.cos(x).sin(x).^(t-1)-... t.cos(x).^(t-1).sin(x)))./(cos(x).^t+sin(x).^t).^2; assert(max(abs((dy-df(x))./dy))<1e-13) end