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Comment on implicit differentiation

The function a(f,x) is sometimes written as  called the partial derivative of g with respect to f keeping x fixed". It can be calculated by differentiating g with respect to f treating x as if it were a constant. 

Similarly b(f,x) is called the partial derivative of g with respect to x keeping f fixed, written as , and is obtained by differentiating g with respect to x as if f were a constant.