# Numerical symbolic differentiation and evaluate at 0.

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I am trying to do numerical symbolic differentiation of the kappa function below after which I want to evaluate at 0 and simplify. This is my code:

clear

syms delta gamma rho lambda T sigma u r

f_1(u) = 1i*u*rho -(1-exp(-lambda*T))*(u^2+1i*u)/(2*lambda);

f_2(u) = 1i*u*rho-(u^2+2*1i*u)/(2*lambda);

I(u) = delta/lambda*(sqrt(gamma^2-2*f_1(u))-sqrt(gamma^2-2*1i*rho*u))...

- 2*delta*f_2(u)/(lambda*sqrt(gamma^2 - 2*f_2(u))) ...

*(atanh(sqrt((gamma^2-2*1i*rho*u)/(gamma^2 - 2*f_2(u)))) ...

- atanh(sqrt( (gamma^2-2*f_1(u))/(gamma^2- 2*f_2(u)))));

kappa(u) = 1i*u*T*(r-lambda*(delta*rho)/(sqrt(gamma^2 -2*rho))) ...

-sigma*(u^2+1i*u)/(2*lambda)*(1-exp(-lambda*T)) ...

+ lambda*I(u);

c_1(u) = diff(kappa,u);

simplify(c_1(0))

But I get the error: Error in MuPAD command: Division by zero. [_power]

It might be a typo, but I am pretty sure there aren't any. In case I have not, and my friend has neither, it is solvable in Mathematica (I do not have access to or ever tried using the program my self). I've tried all sorts of stuff, but I cannot get Matlab to evaluate it.

I have 2014b of course with the symbolic toolbox (but it might be possible for me to update).

Any ideas?

##### 4 Comments

Walter Roberson
on 23 May 2015

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