1、dy=d(lnx/x)

= 1/x* 1/x+lnx*(- 1/x^2)

= 1/x^2( 1-lnx)

2、dy=d(lnx/x)

=[ 1/x* 1/x-lnx*(- 1/x^2)]/x^2

= 1/x^4( 1+lnx)

Extended data:

Parity of function

Let f(x) be a real function, then f is odd function. The following equation applies to all real numbers x:

f(x) =？ f( -？ X) or f( -x) =? -f(x) Geometrically, a odd function is symmetrical about the origin, that is, its graph will not change after rotating 180 degrees around the origin.

Odd function's examples are X, sin(x), sinh(x) and erf(x).

Let f(x) be a real variable function, then f is an even function, if the following equation holds for all real numbers x:

f(x) =？ f( -？ X) Geometrically, an even function will be symmetrical about the Y axis, that is, its graph will not change after being mirrored on the Y axis.

Examples of even functions are |x|, x 2, cos(x) and cosh(sec)(x).

Even functions cannot be bijective mappings.

Periodicity of function

Let the domain of function f(x) be d, and if there is a positive number L, so that for any x∈D, (x ∈ l)∈D and f(x+l)=f(x) are constants, then f(x) is called a periodic function, and l is called the period of f(x). Usually we say that the period of a periodic function refers to the minimum positive period. The domain D of a periodic function is an unbounded interval with at least one side. If d is bounded, the function is not periodic.