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Derivative of:
Derivative of e^(7*x)
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Integral of d{x}:
(x+2)/(x-3)
Graphing y =:
(x+2)/(x-3)
Canonical form:
(x+2)/(x-3)
Identical expressions
(x+ two)/(x- three)
(x plus 2) divide by (x minus 3)
(x plus two) divide by (x minus three)
x+2/x-3
(x+2) divide by (x-3)
Similar expressions
(2*x+2)/(x-3)
(x-2)/(x-3)
(x+2)/(x+3)

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

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

The solution

You have entered [src]

x + 2
-----
x - 3

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

(x + 2)/(x - 3)

Detail solution

Apply the quotient rule, which is:

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

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

5-я производная [src]

    /    2 + x \
120*|1 - ------|
    \    -3 + x/
----------------
           5    
   (-3 + x)

$$\frac{120 \left(1 - \frac{x + 2}{x - 3}\right)}{\left(x - 3\right)^{5}}$$

Simplify

The third derivative [src]

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

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

Simplify