How to evaluate a first/second derivative for 5th order spline?

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Abdul Mannan 2015-9-8

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https://ww2.mathworks.cn/matlabcentral/answers/241233-how-to-evaluate-a-first-second-derivative-for-5th-order-spline

编辑： Abdul Mannan 2015-9-8

I am using 5th order spline for my function. I want to evaluate its first and second derivative. For example, I am using the code as follows

if true
  x = [0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1];
  y = [0,0.7071,1,0.7071,0,-0.7071,-1,-0.7071,0];
  k = 5;   
  sp = spapi( optknt(x,k), x, y );
  xx = 0:.005:1;
  yy = fnval(xx,sp);
   v_o =  2*pi*cos(2*pi*xx); % First Derivative 
   a_o = -(2*pi)^2*sin(2*pi*xx); % Second Derivative 
   plot(xx,yy);
   hold on; figure, plot(xx,v_o);
   plot(diff(yy,1)); hold off % inaccurate first difference
   hold on; figure, plot(xx,a_o); 
   plot(diff(yy,2)); hold off % inaccurate second difference
end

Please, tell me how can I find first and second derivative for 5th order spline. Thanks

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Abdul Mannan 2015-9-8

编辑：Abdul Mannan 2015-9-8

在 MATLAB Online 中打开

OK. I got the answer but I am not erasing the question for the future use.

if true
x = [0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1];
y = [0,0.7071,1,0.7071,0,-0.7071,-1,-0.7071,0];
k = 5;   
sp = spapi( optknt(x,k), x, y );
xx = 0:.005:1;
yy = fnval(xx,sp);
dsp = fnder(sp);  
dyy = fnval(xx,dsp);
ddsp = fnder(sp,2);  
ddyy = fnval(xx,ddsp);
v_o =  2*pi*cos(2*pi*xx); % First Derivative 
a_o = -(2*pi)^2*sin(2*pi*xx); % Second Derivative 
plot(xx,yy);
hold on; figure, plot(xx,v_o); 
plot(xx,dyy), title('first derivative'); hold off
hold on; figure, plot(xx,a_o);
plot(xx,ddyy); title('second derivative'); hold off
end