obvious error in differentiation
2 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
Hi, I have a function as
Z = (T-Tp)*lambdam*u + ((p*(h^2)*gammaw)/k2) + ((p^2)*(h^2)*l*alpha*r*gammac)/(D*u*C) + (ro*p*(l^2)*u*gammae)/D;
obviously, this function is composed of four terms. I want to divide Z by h (which is a positive, non-zero variable) and then take the derivative of Z with respect to h and put it equal to 0 and get h. so I write the below code:
dh = diff(Z/h,h);
h1 = solve (dh==0,h);
Now I get
h1 = (u*(C*k2*p*(C*D*gammaw*u + alpha*gammac*k2*l*p*r)*(gammae*p*ro*l^2 + T*lambdam*D - Tp*lambdam*D))^(1/2))/(alpha*gammac*k2*l*r*p^2 + C*gammaw*u*D*p)
but if I divide Z by h manually and enter that from the beginning, and then take the derivative, I'll get
h1 = u*((C*k2*(gammae*p*ro*l^2 + T*lambdam*D - Tp*lambdam*D))/(p*(C*D*gammaw*u + alpha*gammac*k2*l*p*r)))^(1/2)
which is consistent with what I get when I do everything manually. Why this happens? what am I missing?
0 Kommentare
Akzeptierte Antwort
Torsten
am 9 Apr. 2022
Did you try
pretty(h1)
and/or
isequal(h1,h2)
( I named the second term h2 ) ?
I think they are equal - at least in h1 you can divide
(C*D*gammaw*u + alpha*gammac*k2*l*p*r)
by
(alpha*gammac*k2*l*r*p^2 + C*gammaw*u*D*p)
to get rid of the quotient .
9 Kommentare
Torsten
am 10 Apr. 2022
Under certain assumptions.
When I "show" that h1 = h2, I use e.g. (a*b)^(1/2) = a^(1/2)*b^(1/2). This only holds if a,b are real (not complex) numbers and non-negative.
I suspect that if such assumptions are necessary, MATLAB does not classify two expressions as equal.
But that's a question for the programmers of the symbolic toolbox - I cannot answer it.
Weitere Antworten (0)
Siehe auch
Kategorien
Mehr zu Assumptions finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!