quad differentiation in matlab

To perform symbolic differentiation in MATLAB, we can use the sym function to convert a mathematical expression into a symbolic expression, and then use the diff function to compute its derivative.

To evaluate the definite integral of a function that cannot be expressed in closed form, we can use numerical integration methods. The quad function in MATLAB is a built-in function for numerical integration using the adaptive Simpson's rule.

To perform quad differentiation using MATLAB, we can combine these two functions by first converting the mathematical expression into a symbolic expression, differentiating it symbolically using diff, and then using the resulting function handle in quad to iteratively integrate and differentiate the function. Here's an example code snippet:

main.m
syms x;
f = sin(x^2); % define a mathematical expression
dfdx = diff(f); % differentiate symbolically
dfdx_fun = matlabFunction(dfdx); % convert to function handle
quad_dfdx = @(x) quad(@(t) dfdx_fun(t), 0, x); % define quad-differentiated function
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In this example, f is a simple mathematical expression, which we differentiate symbolically using diff to obtain dfdx. We then convert dfdx into a function handle using matlabFunction, which allows us to pass it into quad to define a new function quad_dfdx that is both integrated and differentiated. We can evaluate quad_dfdx at different x-values to see its behavior. Note that quad differentiation can quickly become computationally expensive for complex functions or large values of x, so it may not always be a practical solution.