int n = 2;
plot(_1,bessel_J(n,_1).derivative(1)).p1range(0,30);
vector<var> x,y;
for(int i=1; i<10; ++i)
{
  x.push_back(bessel_Jprime_zero(n,i));
  y.push_back(0);
}
mplot(x,y).ac(red).pt(fcircle).legend("Zeroes of Bessel derivative");

These functions are wrappers around the gsl_sf_bessel_XXX functions (Gnu Scientific Library). They are therefore not available if you do not have GSL at compile-time.

function     bessel_J(int n, const function &x);   // blop-function
double       bessel_J(int n, double x);            // evaluate on a number
function     bessel_Y(int n, const function &x);
double       bessel_Y(int n, double x);
function     bessel_I(int n, const function &x);
double       bessel_I(int n, double x);
function     bessel_K(int n, const function &x);
double       bessel_K(int n, double x);
function     bessel_j(int n, const function &x);
double       bessel_j(int n, double x);
function     bessel_y(int n, const function &x);
double       bessel_y(int n, double x);
function     bessel_i_scaled(int n, const function &x);
double       bessel_i_scaled(int n, double x);
function     bessel_k_scaled(int n, const function &x);
double       bessel_k_scaled(int n, double x);

double   bessel_J_zero(int n, int s);    // Return the s-th (nontrivial) zero of the n-th Bessel function
double   bessel_Jprime_zero(int n, int s); // Return the s-th zero of
the 1st derivative of the n-th Bessel J function

 Source files:
   function.h
   function.cc