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Identical expressions
(two /(sqrt(3x+ two -5x)^ two))
(2 divide by ( square root of (3x plus 2 minus 5x) squared ))
(two divide by ( square root of (3x plus two minus 5x) to the power of two))
(2/(√(3x+2-5x)^2))
(2/(sqrt(3x+2-5x)2))
2/sqrt3x+2-5x2
(2/(sqrt(3x+2-5x)²))
(2/(sqrt(3x+2-5x) to the power of 2))
2/sqrt3x+2-5x^2
(2 divide by (sqrt(3x+2-5x)^2))
Similar expressions
(2/(sqrt(3x+2+5x)^2))
(2/(sqrt(3x-2-5x)^2))

The derivative of the function/ (2/(sqrt(3x+2-5x)^2))

Derivative of (2/(sqrt(3x+2-5x)^2))

The solution

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        2         
------------------
                 2
  _______________ 
\/ 3*x + 2 - 5*x

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

2/(sqrt(3*x + 2 - 5*x))^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(\sqrt{- 5 x + \left(3 x + 2\right)}\right)^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\sqrt{- 5 x + \left(3 x + 2\right)}\right)^{2}$ :
  1. Let $u = \sqrt{- 5 x + \left(3 x + 2\right)}$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{- 5 x + \left(3 x + 2\right)}$ :
    1. Let $u = - 5 x + \left(3 x + 2\right)$ .
    2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 5 x + \left(3 x + 2\right)\right)$ :
      1. Differentiate $- 5 x + \left(3 x + 2\right)$ term by term:
        
        Differentiate $3 x + 2$ term by term:
        
        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: $3$
        
        The derivative of the constant $2$ is zero.
        
        The result is: $3$
        
        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: $-5$
        
        The result is: $-2$
      The result of the chain rule is:
      
      $- \frac{1}{\sqrt{- 5 x + \left(3 x + 2\right)}}$
    The result of the chain rule is:
    
    $-2$
  The result of the chain rule is:
  
  $\frac{2}{\left(- 5 x + \left(3 x + 2\right)\right)^{2}}$
So, the result is: $\frac{4}{\left(- 5 x + \left(3 x + 2\right)\right)^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       4        
----------------
               2
(3*x + 2 - 5*x)

$$\frac{4}{\left(- 5 x + \left(3 x + 2\right)\right)^{2}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

    6    
---------
        4
(-1 + x)

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

Simplify

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Derivative of (2/(sqrt(3x+2-5x)^2))

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