derivative plot of function

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shiv gaur
shiv gaur 2022-1-21
回答： Vidhi Agarwal 2024-11-27
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
  2 个评论
Geoff Hayes
Geoff Hayes 2022-1-21
@shiv gaur - please clarify your question. Are you asking how to determine the derivative of the function with respect to t?

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回答（1 个）

Vidhi Agarwal
Vidhi Agarwal 2024-11-27
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!

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