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(5-2*x)/(3*x+7)

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Derivative of:
Derivative of x^2*cos(2*x)
Derivative of ((x-1)/(x+1))^4
Derivative of (x-1)/(2*x+3)
Derivative of sqrt(x)^2-2*x
Identical expressions
(five - two *x)/(three *x+ seven)
(5 minus 2 multiply by x) divide by (3 multiply by x plus 7)
(five minus two multiply by x) divide by (three multiply by x plus seven)
(5-2x)/(3x+7)
5-2x/3x+7
(5-2*x) divide by (3*x+7)
Similar expressions
(5+2*x)/(3*x+7)
(5-2*x)/(3*x-7)

The derivative of the function/ (5-2*x)/(3*x+7)

Derivative of (5-2x)/(3x+7)

The solution

You have entered [src]

5 - 2*x
-------
3*x + 7

$$\frac{5 - 2 x}{3 x + 7}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 5 - 2 x$ and $g{\left(x \right)} = 3 x + 7$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $5 - 2 x$ term by term:
  1. The derivative of the constant $5$ 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: $-2$
  The result is: $-2$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $3 x + 7$ term by term:
  1. The derivative of the constant $7$ 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: $3$
Now plug in to the quotient rule:

$- \frac{29}{\left(3 x + 7\right)^{2}}$

The answer is:

$- \frac{29}{\left(3 x + 7\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2      3*(5 - 2*x)
- ------- - -----------
  3*x + 7             2
             (3*x + 7)

$$- \frac{3 \left(5 - 2 x\right)}{\left(3 x + 7\right)^{2}} - \frac{2}{3 x + 7}$$

Simplify

The second derivative [src]

  /    3*(-5 + 2*x)\
6*|2 - ------------|
  \      7 + 3*x   /
--------------------
              2     
     (7 + 3*x)

$$\frac{6 \left(- \frac{3 \left(2 x - 5\right)}{3 x + 7} + 2\right)}{\left(3 x + 7\right)^{2}}$$

Simplify

The third derivative [src]

   /     3*(-5 + 2*x)\
54*|-2 + ------------|
   \       7 + 3*x   /
----------------------
               3      
      (7 + 3*x)

$$\frac{54 \left(\frac{3 \left(2 x - 5\right)}{3 x + 7} - 2\right)}{\left(3 x + 7\right)^{3}}$$

Simplify

The graph

Derivative of (5-2*x)/(3*x+7)