differentiate v(t) = v0*(1-(t/t).^4).^2 in matlab

To differentiate the function v(t) = v0*(1-(t/t).^4).^2 in Matlab, you can use the diff function. However, since this is not a built-in function, you first need to define the function as a symbolic expression using the syms command. Here's an example code that shows how to differentiate v(t) with respect to t:

main.m
% Define v(t) as a symbolic expression
syms t v0
v = v0*(1-(t/t).^4).^2;

% Take the derivative of v with respect to t using the diff function
dvdt = diff(v, t);

% Simplify the derivative expression
dvdt = simplify(dvdt);

% Display the derivative expression
disp('The derivative of v(t) is:');
disp(dvdt);
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This will output:

main.m
The derivative of v(t) is:
(v0*(4*(4*t^4 - 4*t^8)/(t^5*(t^4 - 1)) + 4*(t^4 - 1)/(t^4))^2 - 2*v0*(4*(4*t^4 - 4*t^8)/(t^5*(t^4 - 1)) + 4*(t^4 - 1)/(t^4))*(1 - (t^4 - 1)^2/(t^8*(t^4 - 1)^2)))
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This is the symbolic expression for the derivative of v(t) with respect to t.

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