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

The derivative of the function/ (3-x^2)/(x+1)

Derivative of (3-x^2)/(x+1)

The solution

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     2
3 - x 
------
x + 1

$$\frac{3 - x^{2}}{x + 1}$$

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

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 3 - x^{2}$ and $g{\left(x \right)} = x + 1$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $3 - x^{2}$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $- 2 x$
  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:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

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Derivative of (3-x^2)/(x+1)

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The solution