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| Total Derivative http://myanna.in/total-derivative-t865.html |
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| Author: | sritejatheboss [ Mon Aug 31, 2009 2:04 am ] |
| Post subject: | Total Derivative |
The total derivative is the derivative with respect to t of the function y=f(t,u_1,...,u_m) that depends on the variable t not only directly but also via the intermediate variables u_1=u_1(t,u_1,...,u_m),...,u_m=u_m(t,u_1,...,u_m). It can be calculated using the formula (partialy)/(partialt)=(partialf)/(partialt)+(partialf)/(partialu_1)(partialu_1)/(partialt)+...+(partialf)/(partialu_m)(partialu_m)/(partialt). The total derivative of a function f(t,x,y,...) with respect to t is implemented in Mathematica as Dt[f[t, x, y, ...], t]. |
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