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Derivative of:
Derivative of x^2/2x+1
Derivative of log(t-1)
Derivative of e^x/(1+x^2)
Derivative of 8*cos(x)
Graphing y =:
(4*x+7)/(2*x+3)
Identical expressions
(four *x+ seven)/(two *x+ three)
(4 multiply by x plus 7) divide by (2 multiply by x plus 3)
(four multiply by x plus seven) divide by (two multiply by x plus three)
(4x+7)/(2x+3)
4x+7/2x+3
(4*x+7) divide by (2*x+3)
Similar expressions
(4*x-7)/(2*x+3)
(4*x+7)/(2*x-3)

The derivative of the function/ (4*x+7)/(2*x+3)

Derivative of (4x+7)/(2x+3)

The solution

You have entered [src]

4*x + 7
-------
2*x + 3

$$\frac{4 x + 7}{2 x + 3}$$

(4*x + 7)/(2*x + 3)

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 4 x + 7$ and $g{\left(x \right)} = 2 x + 3$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $4 x + 7$ 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: $4$
  The result is: $4$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $2 x + 3$ term by term:
  1. The derivative of the constant $3$ 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: $2$
Now plug in to the quotient rule:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   4      2*(4*x + 7)
------- - -----------
2*x + 3             2
           (2*x + 3)

$$\frac{4}{2 x + 3} - \frac{2 \left(4 x + 7\right)}{\left(2 x + 3\right)^{2}}$$

Simplify

The second derivative [src]

  /     7 + 4*x\
8*|-2 + -------|
  \     3 + 2*x/
----------------
            2   
   (3 + 2*x)

$$\frac{8 \left(-2 + \frac{4 x + 7}{2 x + 3}\right)}{\left(2 x + 3\right)^{2}}$$

Simplify

The third derivative [src]

   /    7 + 4*x\
48*|2 - -------|
   \    3 + 2*x/
----------------
            3   
   (3 + 2*x)

$$\frac{48 \left(2 - \frac{4 x + 7}{2 x + 3}\right)}{\left(2 x + 3\right)^{3}}$$

Simplify