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I am really frustrated over the dy/dx notations.For example,we are taught that it is not a ratio,just an operation performed on $y=f(x)$.Also why do people multiply something by $dx$.For example,$t=1+x^2$,then people use $\frac{dt}{dx}=2x$,then write $dt=2x \times dx$.But $dx$ is a differential of $x$.It can have larger values as well.Then why do poeple confuse del y with $dy$.$dy=f'(x)\times dx$ and del y is the change in $y$ in the function.

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  • $\begingroup$ Any help?I am still stuck $\endgroup$
    – a_i_r
    Nov 8, 2020 at 17:41
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    $\begingroup$ You're looking at a notation invented in the 17th century, used today in various ways. We have a lot written here already on all the parts of your question; you might start with this question, its answers, the questions linked to it, their answers, answers to the duplicate questions, and so forth. If the answers are not there, perhaps you can edit your question to explain in more detail what parts of your question are not answered and why not. $\endgroup$
    – David K
    Nov 8, 2020 at 17:43
  • $\begingroup$ You might want to look at this: math.stackexchange.com/questions/21199/… $\endgroup$ Nov 8, 2020 at 17:46

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