Hello Ekagra,
I guess you have numerical values of the voltage as a function of the discharge/charge capacity, right? In this case, you can compute the first derivative numerically, e.g., using finite central differences as follows, where x and y will be Q and V, respectively.
% Definitions
x = linspace(0, 2*pi);
y = sin(x);
% Compute first derivative
dydx = compute_first_derivative(y, x);
% Plot
figure; hold on;
plot(x, y);
plot(x(2:end), dydx);
xlabel('x', 'interpreter', 'latex')
ylabel('y', 'interpreter', 'latex')
legend({'y(x)', 'dy(x)/dx'}, 'interpreter', 'latex', 'location', 'northeastoutside');
% SUB-PASS FUNCTION
function dxdy = compute_first_derivative(x, y)
% Compute first central derivate using a non-uniform grid
%
% Args:
% x (float): Values for the corresponding grid
% y (float): Grid values
%
% Returns:
% dxdy (float): Value of the first derivate for the given grid and its corresponding values
%
% Author: Alberto Cuadra-Lara
h = y(2:end) - y(1:end-1);
hmax = max(h);
mu = h / hmax;
dxdy = zeros(1, length(h));
dxdy(1) = ((x(2) - x(1)) ./ h(1));
for i = 2:length(mu)-1
dxdy(i) = (mu(i)^2 * x(i+1) - (mu(i)^2 - mu(i+1)^2) * x(i) - mu(i+1)^2 * x(i-1)) / ((mu(i)^2 * mu(i+1) + mu(i) * mu(i+1)^2) * hmax);
end
dxdy(end) = ((x(end) - x(end-1)) ./ h(end));
end
