can i replace automatically derivative of step function with delta function in this MuPAD expression?

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timo 2015-1-19

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/170563-can-i-replace-automatically-derivative-of-step-function-with-delta-function-in-this-mupad-expression

I have initially defined:

    f1(t),f2(t),f3(t),f4(t),f5(t)
    2*t, 2, 5 - t, 1, 6 - t
And then:
    F1(t):=(u0(t)|t=t+1)-(u0(t)|t=t-1);
    F2(t):=(u0(t)|t=t-1)-(u0(t)|t=t-2);
    F3(t):=(u0(t)|t=t-2)-(u0(t)|t=t-4);
    F4(t):=(u0(t)|t=t-4)-(u0(t)|t=t-5);
    F5(t):=(u0(t)|t=t-5)-(u0(t)|t=t-7);

And then I calculate:

diff(f1(t)*F1(t)+f2(t)*F2(t)+f3(t)*F3(t)+f4(t)*F4(t)+f5(t)*F5(t),t);

Which gives:

    2*u0(t + 1) - 2*u0(t - 1) - u0(t - 2) + u0(t - 4) - u0(t - 5) + u0(t - 7) + 2*D(u0)(t - 1) - 2*D(u0)(t - 2) + D(u0)(t - 4) - D(u0)(t - 5) - (t - 5)*(D(u0)(t - 2) - D(u0)(t - 4)) - (t - 6)*(D(u0)(t - 5) - D(u0)(t - 7)) - 2*t*(D(u0)(t - 1) - D(u0)(t + 1))

Is it any way to replace automatically the derivative of step functions above with Dirac function?

Example D(u0)(t - 5) with dirac(t-5) ? Thanx