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Derivative of:
Derivative of (x^2+49)/x
Derivative of sec2x
Derivative of x*e^x-e^x
Derivative of (x-3)/sqrt(x)
Identical expressions
(four *x+ two)/(x- two)
(4 multiply by x plus 2) divide by (x minus 2)
(four multiply by x plus two) divide by (x minus two)
(4x+2)/(x-2)
4x+2/x-2
(4*x+2) divide by (x-2)
Similar expressions
(4*x-2)/(x-2)
((x^2+4x+2)/(x-2))*2^(3/(x-2))
(4*x+2)/(x+2)

The derivative of the function/ (4*x+2)/(x-2)

Derivative of (4*x+2)/(x-2)

The solution

You have entered [src]

4*x + 2
-------
 x - 2

$$\frac{4 x + 2}{x - 2}$$

(4*x + 2)/(x - 2)

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 4 x + 2$ and $g{\left(x \right)} = x - 2$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $4 x + 2$ 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: $4$
  The result is: $4$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 2$ term by term:
  1. The derivative of the constant $-2$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$- \frac{10}{\left(x - 2\right)^{2}}$

The answer is:

$- \frac{10}{\left(x - 2\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  4     4*x + 2 
----- - --------
x - 2          2
        (x - 2)

$$\frac{4}{x - 2} - \frac{4 x + 2}{\left(x - 2\right)^{2}}$$

Simplify

The second derivative [src]

  /     1 + 2*x\
4*|-2 + -------|
  \      -2 + x/
----------------
           2    
   (-2 + x)

$$\frac{4 \left(-2 + \frac{2 x + 1}{x - 2}\right)}{\left(x - 2\right)^{2}}$$

Simplify

The third derivative [src]

   /    1 + 2*x\
12*|2 - -------|
   \     -2 + x/
----------------
           3    
   (-2 + x)

$$\frac{12 \left(2 - \frac{2 x + 1}{x - 2}\right)}{\left(x - 2\right)^{3}}$$

Simplify

3-я производная [src]

   /    1 + 2*x\
12*|2 - -------|
   \     -2 + x/
----------------
           3    
   (-2 + x)

$$\frac{12 \left(2 - \frac{2 x + 1}{x - 2}\right)}{\left(x - 2\right)^{3}}$$

Simplify