If おかげで / "okagede" is an expression that means

> thanks to ...; owing to ...; because of ...;

and the correct (?) kanji that this expression derived from is

> 陰 as in お陰で

which by itself means

> shade; yin; negative; sex organs; secret; shadow

what is the relation between the meaning of the kanji and the expression?

(apparently お蔭で · 御蔭で · 御陰で are also kanji precedents)

Possible clues:

(perhaps 陰 could mean "back" or "behind" in the past?)

(and 陰 is the Yin in YinYang?)
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etymology expressions
What is the etymology of お陰で/おかげで and how does the expression relate to the kanji?
_(Marked this as "community wiki" since it's not my answer, just a
consolodation of long neglected[information in the comments that should be an
answer](https://japanese.meta.stackexchange.com/questions/593/comments-are-
not-for-answers).)_

[This site](http://gogen-allguide.com/o/okagesama.html) states:

>
> おかげさまは、他人から受ける利益や恩恵を意味する「お陰」に「様」をつけて、丁寧にした言葉である。古くから「陰」は神仏などの偉大なものの陰で、その庇護（ひご）を受‌​ける意味として使われている。これは、「御影（みかげ）」が「神霊」や「みたま」「死んだ人の姿や肖像」を意味することにも通じる。接頭語に「お」がついて、「おかげ」とな‌​ったのは室町時代末頃からで、悪い影響をこうむった時にも「おかげさま」が使われるようになったのは江戸時代からである

Revised translation. Please correct as necessary:

> "Okagesama" is a polite expression that takes the term "お陰{かげ}," which in
> this case refers to grace or favors received from others, and adds "さま." The
> term 陰 has traditionally referred to gods or goddesses or other greater
> beings lending their protection. The term 御影{みかげ} can also be used to refer
> to spirits more generally or the appearance of the deceased. The "o" prefix
> has been added and used since the late Muromachi period, and the expression
> has been used in negative situations since the Edo period.

And for your last question, yes, `陰{いん}` is the kanji in
[`陰陽{いんよう}`](http://eow.alc.co.jp/search?q=%E9%99%B0%E9%99%BD&ref=sa), which
is the Japanese compound for what we refer to in English as "[yin and
yang](http://en.wikipedia.org/wiki/Yin_and_yang)".
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