- #1
NoahsArk
Gold Member
- 237
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I am confused about implicit differenciation in a few ways. The main confusion is why, in the equation ## x^2 + y^2 = 1 ##, when we are taking the derivative of the left side, ## 2x + 2yy\prime ##, are we adding a ## y\prime ## to the 2y but we aren't adding an ## x\prime ## to the 2x? I also don't even understand what it means to be taking the derivative of the ## y^2 ## portion of this equation. In a regular differentiation example, like finding the derivative of the function ## y = x^2 ##, we are asking what the slope of the curve is on the graph of that function for any given x value. In all the examples I've seen, the derivative is expressed in terms of x. What are we really asking when we are asking what the derivative of ## y^2 ## is? Are we assuming that now x is a function of y instead of y being a function of x like it is in normal differentiation? E.g. in the function ## x = y^2 ## the derivative of this function would be 2y. Thanks