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Identical expressions
three /(two x+ three)^2
3 divide by (2x plus 3) squared
three divide by (two x plus three) squared
3/(2x+3)2
3/2x+32
3/(2x+3)²
3/(2x+3) to the power of 2
3/2x+3^2
3 divide by (2x+3)^2
Similar expressions
3/(2x-3)^2

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

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

The solution

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

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

d /    3     \
--|----------|
dx|         2|
  \(2*x + 3) /

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(2 x + 3\right)^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 3\right)^{2}$ :
  1. Let $u = 2 x + 3$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 3\right)$ :
    1. Differentiate $2 x + 3$ 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: $2$
      2. The derivative of the constant $3$ is zero.
      The result is: $2$
    The result of the chain rule is:
    
    $8 x + 12$
  The result of the chain rule is:
  
  $- \frac{8 x + 12}{\left(2 x + 3\right)^{4}}$
So, the result is: $- \frac{3 \cdot \left(8 x + 12\right)}{\left(2 x + 3\right)^{4}}$
Now simplify:

$\frac{12}{\left(- 2 x - 3\right)^{3}}$

The answer is:

$\frac{12}{\left(- 2 x - 3\right)^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3*(-12 - 8*x)
-------------
           4 
  (2*x + 3)

$$\frac{3 \left(- 8 x - 12\right)}{\left(2 x + 3\right)^{4}}$$

Simplify

The second derivative [src]

    72    
----------
         4
(3 + 2*x)

$$\frac{72}{\left(2 x + 3\right)^{4}}$$

Simplify

The third derivative [src]

  -576    
----------
         5
(3 + 2*x)

$$- \frac{576}{\left(2 x + 3\right)^{5}}$$

Simplify

The graph

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