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Derivative of:
Derivative of x^-6
Derivative of (x+3)/(x-3)
Derivative of (x^3)'
Derivative of log(x^4+x)
Identical expressions
(eleven)/(4x+ one)^ two
(11) divide by (4x plus 1) squared
(eleven) divide by (4x plus one) to the power of two
(11)/(4x+1)2
11/4x+12
(11)/(4x+1)²
(11)/(4x+1) to the power of 2
11/4x+1^2
(11) divide by (4x+1)^2
Similar expressions
(11)/(4x-1)^2

The derivative of the function/ (11)/(4x+1)^2

Derivative of (11)/(4x+1)^2

The solution

You have entered [src]

    11    
----------
         2
(4*x + 1)

$$\frac{11}{\left(4 x + 1\right)^{2}}$$

11/(4*x + 1)^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(4 x + 1\right)^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x + 1\right)^{2}$ :
  1. Let $u = 4 x + 1$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x + 1\right)$ :
    1. Differentiate $4 x + 1$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $4$
      2. The derivative of the constant $1$ is zero.
      The result is: $4$
    The result of the chain rule is:
    
    $32 x + 8$
  The result of the chain rule is:
  
  $- \frac{32 x + 8}{\left(4 x + 1\right)^{4}}$
So, the result is: $- \frac{11 \left(32 x + 8\right)}{\left(4 x + 1\right)^{4}}$
Now simplify:

$\frac{88}{\left(- 4 x - 1\right)^{3}}$

The answer is:

$\frac{88}{\left(- 4 x - 1\right)^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

11*(-8 - 32*x)
--------------
           4  
  (4*x + 1)

$$\frac{11 \left(- 32 x - 8\right)}{\left(4 x + 1\right)^{4}}$$

Simplify

The second derivative [src]

   1056   
----------
         4
(1 + 4*x)

$$\frac{1056}{\left(4 x + 1\right)^{4}}$$

Simplify

The third derivative [src]

 -16896   
----------
         5
(1 + 4*x)

$$- \frac{16896}{\left(4 x + 1\right)^{5}}$$

Simplify