CODEWITHSUNDEEP
wolfram-mathematicaderivative
RRTG
RRTG

Reputation: 35

Why is Mathematica producing a seemingly wrong answer for a derivative?

I'm puzzled by what I think is a mistake in a partial derivative I'm having Mathematica do for me.

Specifically, this is what I have: Derivative I'd like to take

I'm trying to take the partial derivative of the following w.r.t. the variable θ (apologies for the formatting):

f=(1/4)(-4e((1+θ)/2)ψ+eN((1+θ)/2)ψ+eN((1+θ)/2-θd)ψ)-s

But the solution Mathematica produces seems very different from the one I get when I take the derivative myself. While Mathematica says the partial derivative of f w.r.t. θ is:

(1/4)eψ(N-2)

By hand, I get and am quite confident the correct answer is instead:

(1/4)eψ(N(1-d)-2)

That is, Mathematica is producing something that drops the variable d when it is differentiating. I've explored different functions that take a derivative in Mathematica, and the possibility that maybe some of the variables I'm using (such as d) might be protected or otherwise special, but I can't say that I know why the answer's so off. This is the first time in the notebook that d appears, so it is not set to 0. For context, I'm trying to confirm that the derivative of the function is positive for values of the variables in certain ranges, and we have d>0 and d<(1/2). Doing this all by hand works but I'm trying to confirm with Mathematica as I will be dealing with more complicated functions and need to make sure I'm having Mathematica produce the right derivatives.

Upvotes: 1

Views: 577

Answers (1)

Stratubas
Stratubas

Reputation: 3067

Your didn't add spaces in eN and θd, so it thinks they're some other 2-character variables.

Adding spaces between them gives your expected result:

f[θ,e,N,ψ,d,s] = (1/4) (-4 e ((1+θ)/2) ψ + e N ((1+θ)/2) ψ + e N ((1+θ)/2 - θ d) ψ) - s;
D[f[θ, e, N, ψ, d, s], θ] // FullSimplify
(* 1/4 e (-2 + N - d N) ψ *)

Upvotes: 2

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