I'm having some trouble with the terminology used in calculus.(adsbygoogle = window.adsbygoogle || []).push({});

My book states:"Fortunately we don't need to solve an equation for Y in terms of X in order to find the derivative of Y. Instead we can use the method of implicit differentiation. This consists of differentiating both sides of the equation with respect to X and then solving the resulting equation for Y'."

And:"In the examples and exercises of this section it is always assumed that the given equation determines Y implicitly as a differentiable function of X so that the method of implicit differentiation can be applied."

I don't quite understand what they are telling me here. What does"differentiating with respect to X"and"Y as a differentiable function of X"mean?

If it helps explain the above, here's an example equation from the section: X^{2}+Y^{2}= 25

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# Implicit Differentiation: Differentiating in Terms of X

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