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This is wonderful question I came across whiles doing calculus. We all know that $$\frac{d(AB)}{dt} = B\frac{dA}{dt} + A\frac{dB}{dt}.$$ Now if $A=B$ give an example for which $$\frac{dA^2} {dt} \neq 2A\frac{dA}{at}.$$

I have tried many examples and could't get an example, any help?

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    I don't think it is possible; d(AA)/dt= AdA/dt+ AdA/dt=2AdA/dt.2011-11-15
  • 0
    Well I think so too...2011-11-15

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