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Derivative of:
Derivative of sin(x)*cos(x)+x
Derivative of sin^2*2x
Derivative of ln(x+3)
Derivative of log(x^2+5*sqrt(x)-3)
Graphing y =:
(x-1)/(x+3)^2
Identical expressions
(x- one)/(x+ three)^ two
(x minus 1) divide by (x plus 3) squared
(x minus one) divide by (x plus three) to the power of two
(x-1)/(x+3)2
x-1/x+32
(x-1)/(x+3)²
(x-1)/(x+3) to the power of 2
x-1/x+3^2
(x-1) divide by (x+3)^2
Similar expressions
(x-1)/(x-3)^2
(x+1)/(x+3)^2

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

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

The solution

You have entered [src]

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

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

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

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
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: $1$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = x + 3$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 3\right)$ :
  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: $1$
  The result of the chain rule is:
  
  $2 x + 6$
Now plug in to the quotient rule:

$\frac{- \left(x - 1\right) \left(2 x + 6\right) + \left(x + 3\right)^{2}}{\left(x + 3\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1       (-6 - 2*x)*(x - 1)
-------- + ------------------
       2               4     
(x + 3)         (x + 3)

$$\frac{\left(- 2 x - 6\right) \left(x - 1\right)}{\left(x + 3\right)^{4}} + \frac{1}{\left(x + 3\right)^{2}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /    4*(-1 + x)\
6*|3 - ----------|
  \      3 + x   /
------------------
            4     
     (3 + x)

$$\frac{6 \left(- \frac{4 \left(x - 1\right)}{x + 3} + 3\right)}{\left(x + 3\right)^{4}}$$

Simplify

The graph

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