Taking derivatives implicitly is a process saved for instances in which the function in question is not set out or able to be changed into a y = x format.

Take, for example, a function like this:

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No matter what is done to this function, x and y cannot be completely separated onto their own sides into a y = x format. Therefore, the only way to take the derivative of this function is to take the derivative implicitly.

Taking an implicit derivative is nearly identical to that of taking a derivative normally, except you must multiply all derivatives of y by dy/dx.

Here is how you take the derivative of the above function:

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