Mister Exam

Derivative of (x+1)/x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x + 1
-----
  x  
$$\frac{x + 1}{x}$$
(x + 1)/x
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    To find :

    1. Apply the power rule: goes to

    Now plug in to the quotient rule:


The answer is:

The graph
The first derivative [src]
1   x + 1
- - -----
x      2 
      x  
$$\frac{1}{x} - \frac{x + 1}{x^{2}}$$
The second derivative [src]
  /     1 + x\
2*|-1 + -----|
  \       x  /
--------------
       2      
      x       
$$\frac{2 \left(-1 + \frac{x + 1}{x}\right)}{x^{2}}$$
The third derivative [src]
  /    1 + x\
6*|1 - -----|
  \      x  /
-------------
       3     
      x      
$$\frac{6 \left(1 - \frac{x + 1}{x}\right)}{x^{3}}$$
The graph
Derivative of (x+1)/x