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Identical expressions
(three *x- two)/(x+ one)
(3 multiply by x minus 2) divide by (x plus 1)
(three multiply by x minus two) divide by (x plus one)
(3x-2)/(x+1)
3x-2/x+1
(3*x-2) divide by (x+1)
Similar expressions
(3*x-2)/(x-1)
(3*x+2)/(x+1)
2/x+3*x-2/x+1

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

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

The solution

You have entered [src]

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

$$\frac{3 x - 2}{x + 1}$$

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

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $3 x - 2$ term by term:
  1. The derivative of the constant $-2$ 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: $x$ goes to $1$
    So, the result is: $3$
  The result is: $3$
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:

$\frac{5}{\left(x + 1\right)^{2}}$

The answer is:

$\frac{5}{\left(x + 1\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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