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(x+1)^2*(x-5)-6

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Derivative of:
Derivative of x^2+cos(x)
Derivative of (x+1)^2*(x-5)-6
Derivative of log(11*x)
Derivative of e^x-2
Identical expressions
(x+ one)^ two *(x- five)- six
(x plus 1) squared multiply by (x minus 5) minus 6
(x plus one) to the power of two multiply by (x minus five) minus six
(x+1)2*(x-5)-6
x+12*x-5-6
(x+1)²*(x-5)-6
(x+1) to the power of 2*(x-5)-6
(x+1)^2(x-5)-6
(x+1)2(x-5)-6
x+12x-5-6
x+1^2x-5-6
Similar expressions
(x+1)^2*(x-5)+6
(x-1)^2*(x-5)-6
(x+1)^2*(x+5)-6

The derivative of the function/ (x+1)^2*(x-5)-6

Derivative of (x+1)^2*(x-5)-6

The solution

You have entered [src]

       2            
(x + 1) *(x - 5) - 6

$$\left(x - 5\right) \left(x + 1\right)^{2} - 6$$

(x + 1)^2*(x - 5) - 6

Detail solution

Differentiate $\left(x - 5\right) \left(x + 1\right)^{2} - 6$ term by term:
1. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = \left(x + 1\right)^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Let $u = x + 1$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 1\right)$ :
    1. Differentiate $x + 1$ term by term:
      1. Apply the power rule: $x$ goes to $1$
      2. The derivative of the constant $1$ is zero.
      The result is: $1$
    The result of the chain rule is:
    
    $2 x + 2$
  $g{\left(x \right)} = x - 5$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Differentiate $x - 5$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $-5$ is zero.
    The result is: $1$
  The result is: $\left(x - 5\right) \left(2 x + 2\right) + \left(x + 1\right)^{2}$
2. The derivative of the constant $-6$ is zero.
The result is: $\left(x - 5\right) \left(2 x + 2\right) + \left(x + 1\right)^{2}$
Now simplify:

$3 \left(x - 3\right) \left(x + 1\right)$

The answer is:

$3 \left(x - 3\right) \left(x + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

6*(-1 + x)

$$6 \left(x - 1\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of (x+1)^2*(x-5)-6