The discussion centers on the differentiation of a composite function, specifically the expression \(\frac{d}{du} f(u(x,y), v(x,y))\). Participants clarify that inner derivatives are not obtained when differentiating with respect to outer variables, such as \(u\), instead of the inner variables \(x\) and \(y\). The consensus is that the differentiation process does not yield inner derivatives in this context, reinforcing the importance of understanding variable relationships in multivariable calculus.
PREREQUISITESStudents and professionals in mathematics, particularly those studying calculus, as well as educators looking to clarify concepts related to differentiation of composite functions.
I initially assumed I wouldn't get the inner derivatives because I wasn't differentiating with respect to the.. "inner variables". But I can't quite put it down in writing in a way that seems convincing to me, hence the uncertainty.arildno said:You say you're not sure. But you also make the point that you are not differentiating with respect to inner variables.
So, what do you think is the correct answer to your question?