Calculus Help: Implicit Differentiation: xy + sqrt(x+y)=21 - Techniques

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... In fact we always apply Implicit differentiation, even with separable functions, for example y = x^2 ... d/dx [ y ] = d/dx [ x^2 ] ... 1 * y' = 2 * x^(2 - 1) * dx/dx ... y'= 2x ... so differentiation is ALWAYS implicitly executed, but we are not always aware of it, just like in my example, we normally don't mention the derivative of y with respect to x, namely the 1! Your explanation was very clear and systematic, for which I thank you ... Jan-W

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