Mister Exam

Derivative of (3x-2)/(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*x - 2
-------
 x + 1 
$$\frac{3 x - 2}{x + 1}$$
(3*x - 2)/(x + 1)
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. 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:

    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:

    Now plug in to the quotient rule:


The answer is:

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