So far, we have treated relations of the form y = f (x). Examples of such relations are;
y= 3x- 2x+ 1, y=1+ x, In any of these relations, y is said to be expressed explicitly in tems of x. The derivative of y with respect to x can be found from the rules of differentiation which have been discussed in the previous units. Sometimes, the relationship between y and x may not be expressed explicitly. For example, consider x²y + xy² +3x = 0. Here, the relation between y and x is not expressed explicitly. The relationship between y and x is said to be implicit. In differentiating x²y+ xy² + 3x = 0, y is treated as if it is a function of x and the rules of differentiation are applied in the appropriate manner. The process of #differentiating #implicit #functions is called implicit differentiation.
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