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?