matlab 求解 f(x)=x(x+1)(x+2)(x+3)(x+4)...(x+n-2)(x+n-1)(x+n)的导数;

matlab diff()

问题的提出


问题

代码求解

    clc; clear; close all;

    filename='how10.txt';

    syms x; % be careful performance issue.

    fileID = fopen(filename, 'w');

    str="x";

    f=str2sym(str);

    fprintf(fileID,'%s\r\n',string(f));

    result=diff(f,x);

    fprintf(fileID,'%s\r\n',string(result));

    ff=matlabFunction(result);

    fprintf(fileID,'%d\r\n',1);

    fprintf(fileID,'\r\n');

    for i = 1:10

        newstr="*(x+"+int2str(i)+")";

        str=str+newstr;

        f=str2sym(str);

        fprintf(fileID,'%s\r\n',string(f));

        result=diff(f,x);

        fprintf(fileID,'%s\r\n',string(result));

        ff=matlabFunction(result);

        fprintf(fileID,'%f\r\n',ff(0));

        fprintf(fileID,'\r\n');

    end

代码输出

x 原函数

1 导函数

1

x*(x + 1) 原函数

2*x + 1 导函数

1.000000

x*(x + 1)(x + 2)

(x + 1)(x + 2) + x*(x + 1) + x*(x + 2)

2.000000

x*(x + 1)(x + 2)(x + 3)

x*(x + 1)(x + 2) + x(x + 1)(x + 3) + x(x + 2)(x + 3) + (x + 1)(x + 2)*(x + 3)

6.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)

x(x + 1)(x + 2)(x + 3) + x*(x + 1)(x + 2)(x + 4) + x*(x + 1)(x + 3)(x + 4) + x*(x + 2)(x + 3)(x + 4) + (x + 1)(x + 2)(x + 3)*(x + 4)

24.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)

x*(x + 1)(x + 2)(x + 3)(x + 4) + x(x + 1)(x + 2)(x + 3)(x + 5) + x(x + 1)(x + 2)(x + 4)(x + 5) + x(x + 1)(x + 3)(x + 4)(x + 5) + x(x + 2)(x + 3)(x + 4)(x + 5) + (x + 1)(x + 2)(x + 3)(x + 4)*(x + 5)

120.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)

x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 6) + x*(x + 1)(x + 2)(x + 3)(x + 5)(x + 6) + x*(x + 1)(x + 2)(x + 4)(x + 5)(x + 6) + x*(x + 1)(x + 3)(x + 4)(x + 5)(x + 6) + x*(x + 2)(x + 3)(x + 4)(x + 5)(x + 6) + (x + 1)(x + 2)(x + 3)(x + 4)(x + 5)*(x + 6)

720.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)

(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6) + x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 7) + x(x + 1)(x + 2)(x + 3)(x + 4)(x + 6)(x + 7) + x(x + 1)(x + 2)(x + 3)(x + 5)(x + 6)(x + 7) + x(x + 1)(x + 2)(x + 4)(x + 5)(x + 6)(x + 7) + x(x + 1)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7) + x(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)*(x + 7)

5040.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)

(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 8) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 7)(x + 8) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 6)(x + 7)(x + 8) + x*(x + 1)(x + 2)(x + 3)(x + 5)(x + 6)(x + 7)(x + 8) + x*(x + 1)(x + 2)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8) + x*(x + 1)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8) + x*(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)

40320.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8) + x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 9) + x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 8)(x + 9) + x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 7)(x + 8)(x + 9) + x(x + 1)(x + 2)(x + 3)(x + 4)(x + 6)(x + 7)(x + 8)(x + 9) + x(x + 1)(x + 2)(x + 3)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9) + x(x + 1)(x + 2)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9) + x(x + 1)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9) + x(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9) + (x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)*(x + 9)

362880.000000

x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)

x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 10) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 9)(x + 10) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 8)(x + 9)(x + 10) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 7)(x + 8)(x + 9)(x + 10) + x*(x + 1)(x + 2)(x + 3)(x + 4)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10) + x*(x + 1)(x + 2)(x + 3)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10) + x*(x + 1)(x + 2)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10) + x*(x + 1)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10) + x*(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10) + (x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)*(x + 10)

3628800.000000

分析代码结果

可以看出来

结果为

matlab 求解 f(x)=x(x+1)(x+2)(x+3)(x+4)...(x+n-2)(x+n-1)(x+n)的导数;的更多相关文章

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