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d/dx is differentiating something that isn't necessarily an equation denoted by y.
dy/dx is differentiating an equation y with respect to x
dy/dx is a noun. It is the thing you get after taking the derivative of y.
d/dx is a verb. It says "take the derivative of this thing I'm about to write after this"

[QUOTE="MathLover1, post: 1102876, member: 280"] [B]d/dx[/B] is differentiating something that [B]isn't necessarily an equation denoted by y. dy/dx[/B] is differentiating [B]an equation y[/B] with respect to [B]x dy/dx[/B] is a[B] noun[/B]. It is the thing you get after taking the[B] derivative of y[/B]. [B]d/dx[/B] is [B]a verb[/B]. It says "[B]take the derivative [/B]of this thing I'm about to write after this" [/QUOTE]