Confusion about implicit differentiation involving e.

ofchaoticreign

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The chain rule says that the derivative of sin (x^2) = d/dx sin(x^2) times d/dx (x^2). Notice that the (x^2) is the inside f'n, whilst [sin(x^2)] is the outside f'n. Notice the the inside f'n is on the left it is "inside".
But, when it comes to the derivative of something like 5ex/y is 5 times d/dx ex/y times d/dx (x/y). This is kinda confusing to me because they are treating (x/y) as the inside function, and 5e as the outside function. Why is that? Why is the inside f'n is now on the right - the exponent is now the inside f'n? To me this is confusing, since it doesn't fit the definition of the chain rule as usually stated. Is there a reason for this?


Nvm, confusion cleared up. I was looking at it the wrong way.
 
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