Differentiate with Respect to Derivative

Question

Mitra Taghizadeh 2022-9-12

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https://ww2.mathworks.cn/matlabcentral/answers/1803220-differentiate-with-respect-to-derivative

评论： Mitra Taghizadeh 2022-9-13

Hi,

I have this code:

syms x(t) m k t 
T = m/2*diff(x(t),t)^2;
D1 = diff(T,diff(x(t), t))

But I got this error:

Second argument must be a variable or a nonnegative integer specifying the number of differentiations.

Do you know how can I have the differentiate with respect to derivative?!

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Answer 1

David Goodmanson 2022-9-12

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https://ww2.mathworks.cn/matlabcentral/answers/1803220-differentiate-with-respect-to-derivative#answer_1051640

在 MATLAB Online 中打开

Hello Mitra,

what version of Matlab are you running? Running your code in 2021b gives

    D1 =
    m*diff(x(t), t)

as desired. Running it in 2019b gives the error message that you have. So there must have been some improvements in the interim. The following workaround, though, runs in 2019b and gives the correct result:

syms x(t) m k t dxdt 
T = m/2*diff(x(t),t)^2;
T = subs(T,diff(x(t),t),dxdt);
D1 = diff(T,dxdt);
D1 = subs(D1,dxdt,diff(x(t),t))
    D1 =
    m*diff(x(t), t)