Mister Exam

Derivative of y*log(y)-y

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
y*log(y) - y
$$y \log{\left(y \right)} - y$$
y*log(y) - y
Detail solution
  1. Differentiate term by term:

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; to find :

      1. The derivative of is .

      The result is:

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result is:


The answer is:

The graph
The first derivative [src]
log(y)
$$\log{\left(y \right)}$$
The second derivative [src]
1
-
y
$$\frac{1}{y}$$
The third derivative [src]
-1 
---
  2
 y 
$$- \frac{1}{y^{2}}$$
The graph
Derivative of y*log(y)-y