Differentiation Equation- result of Derivative-Multi variable

Question

vu ngothanh 2015-4-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/203865-differentiation-equation-result-of-derivative-multi-variable

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

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Jan 2015-4-16

Please remove the copy of the question: http://www.mathworks.com/matlabcentral/answers/203909-differentiation-equation-result-of-derivative-multi-variable-1

vu ngothanh 2015-4-17

Sorry about my annoying. I forget the "edit" component.

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Answer 1

Mischa Kim 2015-4-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/203865-differentiation-equation-result-of-derivative-multi-variable#answer_175566

在 MATLAB Online 中打开

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)