Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^(-x^2)
Derivative of x^2/4
Derivative of -e^-x
Derivative of (x)^(1/2)
Integral of d{x}:
(x+5)/(x+3)
Identical expressions
(x+ five)/(x+ three)
(x plus 5) divide by (x plus 3)
(x plus five) divide by (x plus three)
x+5/x+3
(x+5) divide by (x+3)
Similar expressions
(x+5)/(x-3)
(x-5)/(x+3)

The derivative of the function/ (x+5)/(x+3)

Derivative of (x+5)/(x+3)

The solution

You have entered [src]

x + 5
-----
x + 3

$$\frac{x + 5}{x + 3}$$

(x + 5)/(x + 3)

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x + 5$ term by term:
  1. The derivative of the constant $5$ 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:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1      x + 5  
----- - --------
x + 3          2
        (x + 3)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /    5 + x\
6*|1 - -----|
  \    3 + x/
-------------
          3  
   (3 + x)

$$\frac{6 \left(1 - \frac{x + 5}{x + 3}\right)}{\left(x + 3\right)^{3}}$$

Simplify

The graph

Derivative of (x+5)/(x+3)