How to make syms functions have specific values

For example, there is a function F(x) which has F(0) = 0 and F'(0) = 1. I want to calculate the value of the derivative G'(0) of G(x) = 1/F(x) (this is the example), how do I write the code?

syms F(x)
G(x)=1/F(x)
dG=diff(G)
F(0)=0??
dG(0)

Answer 1

[Star Strider]

One approach —

syms c F(x) x 
dF = diff(F)

dF(x) = 

F(x) = dsolve(dF == c, F(0)==0)

F(x) = 

c = solve(diff(F)==1,c)                     % Determine 'c’

c = 

1

F = subs(F)

F(x) = 

x

G(x) = 1/F(x)

G(x) = 

dG = diff(G)

dG(x) = 

Evaluating ‘dG(0)’ of course results in a division-by-zero error, so it is indeterminate,

Lim_dG = limit(dG, x, 0)

Lim_dG = 

and so is the limit.

There might be other approaches to solving this, for example incorporating a constant-of-integration and the evaluating it as well. However since this was not presented as an integral with integration bounds, I use this approach.

If a better apporoach is posted, I will delete my Answer.

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