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Derivative of (x^2+24)/(x+1)
Graphing y =:
(x^2+24)/(x+1)
Identical expressions
(x^ two + twenty-four)/(x+ one)
(x squared plus 24) divide by (x plus 1)
(x to the power of two plus twenty minus four) divide by (x plus one)
(x2+24)/(x+1)
x2+24/x+1
(x²+24)/(x+1)
(x to the power of 2+24)/(x+1)
x^2+24/x+1
(x^2+24) divide by (x+1)
Similar expressions
(x^2-24)/(x+1)
(x^2+24)/(x-1)

The derivative of the function/ (x^2+24)/(x+1)

Derivative of (x^2+24)/(x+1)

The solution

You have entered [src]

 2     
x  + 24
-------
 x + 1

$$\frac{x^{2} + 24}{x + 1}$$

  / 2     \
d |x  + 24|
--|-------|
dx\ x + 1 /

$$\frac{d}{d x} \frac{x^{2} + 24}{x + 1}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{2} + 24$ and $g{\left(x \right)} = x + 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{2} + 24$ term by term:
  1. The derivative of the constant $24$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$\frac{- x^{2} + 2 x \left(x + 1\right) - 24}{\left(x + 1\right)^{2}}$

The answer is:

$\frac{- x^{2} + 2 x \left(x + 1\right) - 24}{\left(x + 1\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2              
  x  + 24     2*x 
- -------- + -----
         2   x + 1
  (x + 1)

$$\frac{2 x}{x + 1} - \frac{x^{2} + 24}{\left(x + 1\right)^{2}}$$

Simplify

The second derivative [src]

  /          2         \
  |    24 + x      2*x |
2*|1 + -------- - -----|
  |           2   1 + x|
  \    (1 + x)         /
------------------------
         1 + x

$$\frac{2 \left(- \frac{2 x}{x + 1} + 1 + \frac{x^{2} + 24}{\left(x + 1\right)^{2}}\right)}{x + 1}$$

Simplify

The third derivative [src]

  /           2         \
  |     24 + x      2*x |
6*|-1 - -------- + -----|
  |            2   1 + x|
  \     (1 + x)         /
-------------------------
                2        
         (1 + x)

$$\frac{6 \cdot \left(\frac{2 x}{x + 1} - 1 - \frac{x^{2} + 24}{\left(x + 1\right)^{2}}\right)}{\left(x + 1\right)^{2}}$$

Simplify

The graph

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Derivative of (x^2+24)/(x+1)

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The solution