Mister Exam

Derivative of y(ln(y)-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
y*(log(y) - 1)
$$y \left(\log{\left(y \right)} - 1\right)$$
y*(log(y) - 1)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Differentiate term by term:

      1. The derivative of is .

      2. The derivative of the constant is zero.

      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(ln(y)-1)