Derivative after Numerical Integral

hello everyone,

I have a function of x, however I get it after calculating a numerical integral, such as:

a = @(x) (integral(@(x1) sqrt((x+4).*(x1+2)./(x1+1)),0,1))

I need to take the derivative of a in terms of x, and then I calculate the values of diff(a) for different x values.

Any help will be appreciated.

Answer 1

[Star Strider]

Try this:

dfdx = @(f,x) (f(x + 1E-8) - f(x)) ./ 1E-8;                                     % Simple Numeric Derivative
a = @(x) (integral(@(x1) sqrt((x+4).*(x1+2)./(x1+1)),0,1, 'ArrayValued',1))

x = linspace(-1, 1, 25);
dadx = dfdx(a,x);

figure
plot(x, dadx)
grid

Make appropriate changes to ‘x’ for your needs.

EDIT —

You can also use the gradient (link) function to calculate the derivative of a (regularly-spaced) vector of values proeuced by your ‘a’ function.