Differentiation Equation- result of Derivative-Multi variable

2 次查看（过去 30 天）
vu ngothanh
vu ngothanh 2015-4-16
编辑： vu ngothanh 2015-4-17
I have math like this:
L=5
x=5*L^2 %x=125
I need to have a result of y; y=diff(x)=50
Mr. Mischa has just help me to solve it:
syms y(x) % define y as a function of x symbolically
L = 5;
y = 5*x^2; % define the function y
dy = diff(y,x); % compute its derivative
dyL = subs(dy,x,L) % compute the derivative at x = L
But now, I have a same requirement, like the upper one. but it have multi varialble like this:
a=(((m*w^2-k)/(E*mI))^2+(c*w/(E*mI))^2)^(1/8);
b= atan(-c*w/(m*w^2-k))/4+pi/4;
X=a*cos(b);
Y=a*sin(b);
sa=cosh(L*X)*cos(L*Y);
sb=sinh(L*X)*sin(L*Y);
HOw can I get X',Y',sa',sb'. (with m,w,mi,k,c,and E are constant) I don't know the name of this derivative. but it's result like that
X'=a'*cos(b)-a*b'*sin(b)
Y'=a'*sin(b)+a*b'*cos(b)
sa'=L*X'*cos(L*Y)*sinh(L*X)-L*Y'*sin(L*Y)*cosh(L*X)
sb'=L*Y'*cos(L*Y)*sinh(L*X)+L*X'*sin(L*Y)*cosh(L*Y)
I don't know how to say this derivative's name in ENGLISH. After the matlab calculate 4 equation, I insert the number of e,m,c,k,mI... in to the equation, then I get the finally result. w is independent variable.
My first target of these question is solve a very very long equation.
So, I want to decrease the rick of wrong equation when I typing, thus I must split a long equation into many smaller equation. With a normal formular, it is ok. but, when I derivative it, there are a problem. because, matlab with calculate that smaller eq become a number, then matlab derivative it become zero.
Such as, I have a velocity of 1 element, I derivative it, I get the acceleration.
So, the velocity is easy to get by some normal eq, but the accelerator, I must to derivative those eq. That is the problem of mine.
I has just learning about matlab for a week. Sorry about my complex. Thank you very much
  3 个评论
显示 1更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Mischa Kim
Mischa Kim 2015-4-17
Vu, see the example below.
syms a(t) b(t) X t
X = a*cos(b);
dX = diff(X)
dX(t) =
cos(b(t))*diff(a(t), t) - sin(b(t))*a(t)*diff(b(t), t)
  1 个评论
vu ngothanh
vu ngothanh 2015-4-17
Mr. Mischa, my first target of these question is solve a very very long equation.
So, I want to decrease the rick of wrong equation when I typing, thus I must split a long equation into many smaller equation. With a normal formular, it is ok. but, when I derivative it, there are a problem. because, matlab with calculate that smaller eq become a number, then matlab derivative it become zero.
Such as, I have a velocity of 1 element, I derivative it, I get the acceleration.
So, the velocity is easy to get by some normal eq, but the accelerator, I must to derivative those eq. That is the problem of mine.
I has just learning about matlab for a week. Sorry about my complex. Thank you very much

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by