Find $x$ by solving the equation $$\frac{d (x^{2})}{dx} = 2$$

How should I write the remaining steps of the solution?

Should it be

$\implies 2x = 2$

$\implies x= 1$


i.e. $2x=2$

i.e. $x=1$


or $2x=2$

or $x=1$


$\therefore 2x=2$

$\therefore x=1$

Which notations are appropriate?

  • 1
    $\begingroup$ Your first one would be most normal in my opinion. The second one I have never seen. And the $\therefore$ is generally used for a "final important conclusion." I think it's technically correct for the third one, but very non-traditional. $\endgroup$
    – Pavan C.
    Feb 12 at 5:17
  • $\begingroup$ Isn't the result $x=2$? $\endgroup$ Feb 12 at 5:56
  • $\begingroup$ @PavanC. Okay, thanks. $\endgroup$
    – Sasikuttan
    Feb 12 at 6:03
  • 2
    $\begingroup$ You can leave out the symbols altogether —thus reducing visual clutter and improving readability— by simply writing (something like) "We can get to the answer via the following steps:". If individual steps might need later commentary or clarification, be sure to mark them with equation numbers (\tag{#} in TeX or MathJax). ... Of the given options, the first is best. (I tend to use "$\to$" instead of the heavier "$\implies$", and I'd add extra whitespace between symbol and equation.) The second and third are too much of a mix of words and symbols; the fourth is an overuse of "therefore". $\endgroup$
    – Blue
    Feb 12 at 6:41
  • 2
    $\begingroup$ It's worth noting the adage "Know your audience". Writing every step is important to guide unfamiliar readers (eg, students) through manipulations, or to highlight a particularly clever trick; it's also important if there may be a mistake that needs to be detected. But, if your audience knows Calculus, then walking through basic algebraic steps wastes their time; just write "and so $x=1$". If there's a bit of work involved: "one can show that $x=1$". Indeed, authors often skip-over even non-trivial arguments with the somewhat cliché "showing this is left as an exercise to the reader". :) $\endgroup$
    – Blue
    Feb 12 at 7:06


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