I came upon a question where the solution shows that $\alpha$d$\theta$ = ($\theta$ + 1)d($\theta$ +1) becomes ad$\theta$ = ($\theta$ + 1)d$\theta$. I am a little lost as to how this occurs. Was the part of d($\theta$ + 1) differentiated without respect to any variable so that what you are left with is d$\theta$ or was there some other manipulation that occured?
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$\frac d{dx}f(x)=f'(x)\implies df(x)=f'(x)dx$, just as a guide to how people write these things. – lulu Sep 11 '22 at 01:26
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1The point is that $\frac d{d\theta}(\theta+1) = 1$, so $d(\theta+1) = 1,d\theta$. – Ted Shifrin Sep 11 '22 at 01:30
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Here's a primer on differentials, i.e. differentiation without respect to a specific variable. – greg Sep 12 '22 at 16:46