# how to differentiate this function

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shiv gaur on 7 May 2022
ph=t-z+2*tan(z/zr)-(z/zr)*(r/r0*f)^2;
a=r*exp(-r^2/r0^2*f^2)*cos(ph);
how to differentiate with r in matlab
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Sam Chak on 8 May 2022
@shiv gaur, can you share the link, where a MATLAB function can be used to differentiate symbolic expression or function? This helps me to find a relevant example and help you to solve the mathematical problem.

KSSV on 8 May 2022
syms ph(t,z,zr,r,r0,f) a(r,f,r0,ph)
ph = t-z+2*tan(z/zr)-(z/zr)*(r/r0*f)^2;
a = r*exp(-r^2/r0^2*f^2)*cos(ph);
dphdr = diff(ph,r)
dphdr =

Riccardo Scorretti on 8 May 2022
Assuming that you want to differentiate ph and a with respect of r, you have several options (and the best option depends on what you want to do: we cannot know in your place):
1. use your own brain: compute the derivative and program it by hand,
2. let MATLAB to do it at your place, if you have the Symbolic Computational Toolbox,
3. derive numerically (this is not elegant and somehow dangerous).
As for the option 2:
syms r z zr r0 f t
ph = t-z+2*tan(z/zr)-(z/zr)*(r/r0*f)^2;
a = r*exp(-r^2/r0^2*f^2)*cos(ph);
ph_r = diff(ph, r)
ph_r =
a_r = diff(a, r)
a_r =
Then, you can even ask to Matlab to program the numerical computation in your place:
matlabFunction([a_r phi_r], 'File', 'my_function.m');
As for the option 3, basically you can use finite differences:
fun_ph = @(r) t-z+2*tan(z/zr)-(z/zr)*(r/r0*f)^2;
fun_a = @(r) r*exp(-r^2/r0^2*f^2)*cos(ph);
dr = 1.0E-6; % *** this may be tricky to choice ***
fun_ph_r = @(r) (fun_ph(r+dr) - fun_ph(r)) / dr;
fun_a_r = @(r) (fun_a(r+dr) - fun_a(r) ) / dr;
This is the simplest example (= first order, forward finite differences). You can enjoy a more detailed analysis, and high order formulas, here: ChE 205 — Formulas for Numerical Differentiation

R2022a

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