derivative plot of function

function y=f(p,t)
ea=2.25;

em=0.15+1i*3.2;
theta=1:15;
x=1.5*sin(theta);
ka=sqrt(ea-x.^2);
km=sqrt(em-x.^2);

y=2.*atan(1i.*(1-exp(2*1i.*km.*p))./(1+exp(2*1i.*km.*p)))-2.*atan(1i.*exp(2*1i.*ka.*t)./(1+exp(2*1i.*ka.*t)));
end

when we take p=1:15

plot dy/dt vs p and plot dy/dt /dy/dp vs p

[Geoff Hayes]

@shiv gaur - please clarify your question. Are you asking how to determine the derivative of the function with respect to t?

[shiv gaur]

yes

Answer 1

[Vidhi Agarwal]

Hi @shiv gaur,

To determine the derivative of the function ( y = f(p, t) ) with respect to ( t ), try using "symbolic differentiation" in MATLAB.

Below are the steps that might help you out to derivative of the function and plot it:

• Use symbolic variables for ( p ), ( t ), and any other parameters that might affect the differentiation.
• Use the "diff" function to compute the derivative with respect to ( t ).
• Evaluate the derivative at specific values of ( p ), ( t ), or other parameters.

Sample code is given below:

% Initialize arrays to store evaluated values
p_values = 1:15;
dy_dt_values = zeros(size(p_values));
dy_dp_values = zeros(size(p_values));

% Evaluate the derivatives over the range p = 1:15
t_value = 0.5; % Example value for t

for i = 1:length(p_values)
    dy_dt_sum = 0;
    dy_dp_sum = 0;
    for j = 1:length(theta)
        % Evaluate dy/dt and dy/dp for each theta
        dy_dt_j = diff(y(p, t, ka(j), km(j)), t);
        dy_dp_j = diff(y(p, t, ka(j), km(j)), p);
        
        % Substitute specific values and sum the contributions
        dy_dt_sum = dy_dt_sum + double(subs(dy_dt_j, {p, t}, {p_values(i), t_value}));
        dy_dp_sum = dy_dp_sum + double(subs(dy_dp_j, {p, t}, {p_values(i), t_value}));
    end
    % Store the averaged results
    dy_dt_values(i) = dy_dt_sum / length(theta);
    dy_dp_values(i) = dy_dp_sum / length(theta);
end

To read more about "Symbolic Math Toolbox" and "diff" refer to the following documentation:

• Symbolic Math Toolbox : https://www.mathworks.com/help/releases/R2021b/symbolic
• diff: https://www.mathworks.com/help/releases/R2021b/matlab/ref/diff.html

Hope this helps!