MATLAB: Numeric Derivative – problem entering df

error using mpowernumeric derivative

Hi,

I have a function (e(1)^(cos(x^2))+ln(1+x^2)…I derived it correctly to (2*x/1+x^2)-2*x*sin(x^2)*(e(1)^cos(x^2))

Then I tried to enter it to Matlab in this form:

 df=(2*x./(1+x.^2))-(2*x.*sin(x.^2)*exp(1)^(cos(x.^2)))

But I am still having this error: Error using ==> mpower Inputs must be a scalar and a square matrix. To compute elementwise POWER, use POWER (.^) instead.

I really don't know where else I have to put the dots…

Can somebody fix this expression, please ??

Thanks a lot

Best Answer

df=2*x./(1+x.^2)-2*x.*sin(x.^2).*exp(1).^cos(x.^2)

Related Solutions

MATLAB: ERROR: Index in position 1 exceeds array bounds. Error in mainpgm (line 289) xdata = [DF(1,:);DF(3,:)];, xdata = [DF(2,:);DF(4,:)];

One of the images has no detected face. you break the for loop before appending the DF for that image the remaining images .

MATLAB: Symbolic Math shows weird behavior – not seen in Wolfram or Octave

It looks like the expected solution can be obtained with some work. Maybe someone else can get there faster.

>> syms x real
>> A = sym([1 -2*cos(x) 0; -sin(x)/cos(x)*sin(x) 1 cos(x); 1 -2*sin(x)/cos(x)*sin(x) 2])
 
A =
 
[                1,            -2*cos(x),      0]
[ -sin(x)^2/cos(x),                    1, cos(x)]
[                1, -(2*sin(x)^2)/cos(x),      2]
>> [V,D]=eig(A)
 
V =
 
[ ((cos(x)^4 + 3*cos(x)^2*sin(x)^2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3) + 4/3))/(cos(x)^4 - 2*sin(x)^6) - (2*(cos(x)^4 + cos(x)^2*sin(x)^4 + cos(x)^2*sin(x)^2))/(cos(x)^4 - 2*sin(x)^6) - (cos(x)^2*sin(x)^2*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3) + 4/3)^2)/(cos(x)^4 - 2*sin(x)^6), - (2*(cos(x)^4 + cos(x)^2*sin(x)^4 + cos(x)^2*sin(x)^2))/(cos(x)^4 - 2*sin(x)^6) - ((cos(x)^4 + 3*cos(x)^2*sin(x)^2)*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 + (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3))/(cos(x)^4 - 2*sin(x)^6) - (cos(x)^2*sin(x)^2*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 + (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3)^2)/(cos(x)^4 - 2*sin(x)^6), - (2*(cos(x)^4 + cos(x)^2*sin(x)^4 + cos(x)^2*sin(x)^2))/(cos(x)^4 - 2*sin(x)^6) - ((cos(x)^4 + 3*cos(x)^2*sin(x)^2)*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 - (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3))/(cos(x)^4 - 2*sin(x)^6) - (cos(x)^2*sin(x)^2*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 - (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3)^2)/(cos(x)^4 - 2*sin(x)^6)]
[      ((3*cos(x)^3 + 2*cos(x)*sin(x)^4)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3) + 4/3))/(2*(cos(x)^4 - 2*sin(x)^6)) - (cos(x)^3 + 2*cos(x)*sin(x)^4 + cos(x)^3*sin(x)^2)/(cos(x)^4 - 2*sin(x)^6) - (cos(x)^3*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3) + 4/3)^2)/(2*(cos(x)^4 - 2*sin(x)^6)),      - (cos(x)^3 + 2*cos(x)*sin(x)^4 + cos(x)^3*sin(x)^2)/(cos(x)^4 - 2*sin(x)^6) - ((3*cos(x)^3 + 2*cos(x)*sin(x)^4)*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 + (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3))/(2*(cos(x)^4 - 2*sin(x)^6)) - (cos(x)^3*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 + (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3)^2)/(2*(cos(x)^4 - 2*sin(x)^6)),      - (cos(x)^3 + 2*cos(x)*sin(x)^4 + cos(x)^3*sin(x)^2)/(cos(x)^4 - 2*sin(x)^6) - ((3*cos(x)^3 + 2*cos(x)*sin(x)^4)*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 - (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3))/(2*(cos(x)^4 - 2*sin(x)^6)) - (cos(x)^3*(1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 - (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 4/3)^2)/(2*(cos(x)^4 - 2*sin(x)^6))]
[                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           1,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         1,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         1]
 
 
D =
 
[ 1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) + (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3) + 4/3,                                                                                                                                                                                                                                                                                                                                                                                           0,                                                                                                                                                                                                                                                                                                                                                                                           0]
[                                                                                                                                                                                     0, 4/3 - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 - (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)),                                                                                                                                                                                                                                                                                                                                                                                           0]
[                                                                                                                                                                                     0,                                                                                                                                                                                                                                                                                                                                                                                           0, 4/3 - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)/2 + (3^(1/2)*(1/(9*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3)) - (((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))*1i)/2 - 1/(18*(((cos(x)^2 + sin(x)^2 - 1/27)^2 - 1/729)^(1/2) - cos(x)^2 - sin(x)^2 + 1/27)^(1/3))]
 
>> D=simplify(diag(D),300)  % unclear why D(1) doesn't simplify to 2 - 1i
 
D =
 
 2 - (2*(-1)^(1/3)*(2*3^(1/2) - 3)*(- 15*3^(1/2) - 26)^(1/3))/3 - 3^(1/2)/3
                                                                          0
                                                                     2 + 1i
 
>> V2=V(:,2);  % pick the eigenvector associated with lamda = 0
>> simplify(imag(V2),100)  % verify the imaginary part is 0
 
ans =
 
 0
 0
 0
 
>> V2=real(V2);  % grab the real part
>> V2=simplify(V2,100)
 
V2 =
 
         - 1/cos(2*x) - 1
 -cos(x)/(2*cos(x)^2 - 1)
                        1
 
 
>> simplify(V2*(1-2*sin(x)^2),100)
 
ans =
 
 -2*cos(x)^2
     -cos(x)
    cos(2*x)

Best Answer

Related Solutions

MATLAB: ERROR: Index in position 1 exceeds array bounds. Error in mainpgm (line 289) xdata = [DF(1,:);DF(3,:)];, xdata = [DF(2,:);DF(4,:)];

MATLAB: Symbolic Math shows weird behavior – not seen in Wolfram or Octave

Related Question