- #1

Char. Limit

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## Main Question or Discussion Point

Is it possible to take a derivative with respect to a function, rather than just a variable? I'll give a simple example of how I imagine such a thing would work to try to explain...

[tex]\frac{d}{d(sin(x))}\left(sin^2(x)\right) = 2 sin(x)[/tex]

Can you take a derivative this way?

Also, can you write an equivalent integral as such?

[tex]\int 2 sin(x) d(sin(x)) = sin^2(x) + C[/tex]

[tex]\frac{d}{d(sin(x))}\left(sin^2(x)\right) = 2 sin(x)[/tex]

Can you take a derivative this way?

Also, can you write an equivalent integral as such?

[tex]\int 2 sin(x) d(sin(x)) = sin^2(x) + C[/tex]