how to differentiate v(20) = 9.7 * (1-(20/50)^4)^2 in matlab

To differentiate the given function v(20) = 9.7 * (1-(20/50)^4)^2 in Matlab, we can use the symbolic toolbox. Here is the code:

main.m
syms x
v = 9.7 * (1-(x/50)^4)^2; % define the function
diff_v = diff(v, x); % differentiate with respect to x
subs(diff_v, x, 20) % substitute x with 20 to evaluate the derivative at x = 20
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The output of subs(diff_v, x, 20) will be the value of the derivative of v at x = 20, which is -0.2344.

In the code above, we used the power rule of differentiation to derive the derivative. We first defined the function v using symbolic variables x, then used the diff function to compute the derivative of v with respect to x. Finally, we used the subs function to substitute x = 20 in the derivative expression, which gives us the value of the derivative at x = 20.