The derivation of x on both sides is to regard x as a variable and the others as constants, and then to derive, for example, the function F=xy, the derivation of x means F'=y, and the derivation of y means F'=x,

therefore

1/y * y' = v (x)' lnu (x)+v (x) * u' (x)/u (x) is the derivative of the equation lny=V(x)lnu(x) with respect to x.

Implicit function: in an equation f(x, y)? =? 0, if x takes any value in a certain interval, there is always a corresponding y that satisfies this equation, then it can be said that the equation f(x, y)? =? 0 determines the implicit function y of x in this interval, such as x2? +? y2？ 1? =? 0。 Functions that can be directly expressed by expressions with independent arguments are called explicit functions, which are generally called functions, such as y? =? cos(x).

The simple understanding is that

For example, function F(x, y), if y is a function about x, then function F(x, y) is an implicit function.

This problem is actually to find the implicit function. You can substitute y into the above steps.