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April 11th, 2015, 07:51 AM  #1 
Member Joined: Jul 2012 Posts: 60 Thanks: 0 Math Focus: Calculus  Fake multivariable function notation
So let's say I had a multivariable function, random example: $\displaystyle f(x,t)=x^2 + x\cdot t + \sin{t} $ But what if x was actually a function of t itself. Would the following notation be permitted? $\displaystyle f(x(t),t)=x^2(t) + x(t)\cdot t + \sin{t} $ And also, does that imply the following? $\displaystyle 1^\circ \; f(x(tt_0),t)=x^2(tt_0) + x(tt_0)\cdot t + \sin{t} \\$ $\displaystyle 2^\circ \; f(x(t),tt_0)=x^2(tt_0) + x(tt_0)\cdot (tt_0) + \sin{(tt_0)} $ The first one makes sense, but the second one seems a bit strange. Is there a better way to write this down? Thanks. 
April 11th, 2015, 10:10 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,835 Thanks: 2162 
The first interpretation would be correct.


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