Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of atan(sqrt(x))
Derivative of 3*x^5
Derivative of 3*x^2*e^x
Derivative of 3*cos(3*x)
Graphing y =:
(x^2-3x+2)/(x+1)
Identical expressions
(x^ two -3x+ two)/(x+ one)
(x squared minus 3x plus 2) divide by (x plus 1)
(x to the power of two minus 3x plus two) divide by (x plus one)
(x2-3x+2)/(x+1)
x2-3x+2/x+1
(x²-3x+2)/(x+1)
(x to the power of 2-3x+2)/(x+1)
x^2-3x+2/x+1
(x^2-3x+2) divide by (x+1)
Similar expressions
(x^2-3x-2)/(x+1)
(x^2+3x+2)/(x+1)
(x^2-3x+2)/(x-1)

The derivative of the function/ (x^2-3x+2)/(x+1)

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

The solution

You have entered [src]

 2          
x  - 3*x + 2
------------
   x + 1

$$\frac{\left(x^{2} - 3 x\right) + 2}{x + 1}$$

(x^2 - 3*x + 2)/(x + 1)

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2} - 3 x + 2$ and $g{\left(x \right)} = x + 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} - 3 x + 2$ term by term:
  1. The derivative of the constant $2$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  3. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $-3$
  The result is: $2 x - 3$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$\frac{- x^{2} + 3 x + \left(x + 1\right) \left(2 x - 3\right) - 2}{\left(x + 1\right)^{2}}$
Now simplify:

$\frac{x^{2} + 2 x - 5}{x^{2} + 2 x + 1}$

The answer is:

$\frac{x^{2} + 2 x - 5}{x^{2} + 2 x + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            2          
-3 + 2*x   x  - 3*x + 2
-------- - ------------
 x + 1              2  
             (x + 1)

$$\frac{2 x - 3}{x + 1} - \frac{\left(x^{2} - 3 x\right) + 2}{\left(x + 1\right)^{2}}$$

Simplify

The second derivative [src]

  /         2                 \
  |    2 + x  - 3*x   -3 + 2*x|
2*|1 + ------------ - --------|
  |             2      1 + x  |
  \      (1 + x)              /
-------------------------------
             1 + x

$$\frac{2 \left(1 - \frac{2 x - 3}{x + 1} + \frac{x^{2} - 3 x + 2}{\left(x + 1\right)^{2}}\right)}{x + 1}$$

Simplify

The third derivative [src]

  /                     2      \
  |     -3 + 2*x   2 + x  - 3*x|
6*|-1 + -------- - ------------|
  |      1 + x              2  |
  \                  (1 + x)   /
--------------------------------
                   2            
            (1 + x)

$$\frac{6 \left(-1 + \frac{2 x - 3}{x + 1} - \frac{x^{2} - 3 x + 2}{\left(x + 1\right)^{2}}\right)}{\left(x + 1\right)^{2}}$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

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

The graph:

Piecewise:

The solution