Differentiation for relative sensitivity calculation

I need to differentiate xN with respect to ln (Nd) and plot the result for Nd varying between 10^14/ cm^3 to 10^18/cm^3. Can any one please help. Heartfelt thanks...

K=1.38e-23;
T=300;
q=1.6e-19;
esi=11.8;
e0=8.854e-14;
Na=1e19;
ni=1.1e10;
syms Nd
v=(K*T)/q;
x=((Na.*Nd)./(ni^2));
Vbi=(v.*log(x));
xN=sqrt((2*esi*e0/q)*((Na*Vbi)./(Nd.*(Na+Nd))));

Answer 1

[Stephan]

D_xN = diff(xN,Nd)

[SWASTIK SAHOO]

It's coming all 0.. and how can I plot the differentiation result???

[Stephan]

Run the complete code:

K=1.38e-23;
T=300;
q=1.6e-19;
esi=11.8;
e0=8.854e-14;
Na=1e19;
ni=1.1e10;
syms Nd
v=(K*T)/q;
x=((Na.*Nd)./(ni^2));
Vbi=(v.*log(x));
xN=sqrt((2*esi*e0/q)*((Na*Vbi)./(Nd.*(Na+Nd))));
D_xN = diff(xN,Nd)

To plot:

fplot(D_xN,[-1e4 1e7])

[Stephan]

Also you can use:

>> pretty(xN)

                  /             / 10 Nd \          \
                  |          log| ----- |          |
                  |             \  121  /          |
sqrt(6007439) sqrt| ------------------------------ | 750000000
                  \ Nd (Nd + 10000000000000000000) /

and for the derivative:

>> pretty(D_xN)

                /              / 10 Nd \                                                           / 10 Nd \          \
                |           log| ----- |                                                        log| ----- |          |
                |              \  121  /                           1                               \  121  /          |
  sqrt(6007439) | ------------------------------- - ------------------------------- + ------------------------------- | 375000000
                |                               2     2                                 2                             |
                \ Nd (Nd + 10000000000000000000)    Nd  (Nd + 10000000000000000000)   Nd  (Nd + 10000000000000000000) /
- -------------------------------------------------------------------------------------------------------------------------------
                                                   /             / 10 Nd \          \
                                                   |          log| ----- |          |
                                                   |             \  121  /          |
                                               sqrt| ------------------------------ |
                                                   \ Nd (Nd + 10000000000000000000) /

[SWASTIK SAHOO]

I want to do differentiation between xN and log(Nd) and plot that so that I can see the change in xN with respect to change in Nd. That I am not able to do..Could you please help?? Thank you so much