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Derivative of:
Derivative of e^(6*x)
Derivative of -1/y
Derivative of sin^2(x^2)
Derivative of log(1+1/(x^2))
Sum of series:
1/(2x-1)^2
Integral of d{x}:
1/(2x-1)^2
Graphing y =:
1/(2x-1)^2
Identical expressions
one /(two x- one)^2
1 divide by (2x minus 1) squared
one divide by (two x minus one) squared
1/(2x-1)2
1/2x-12
1/(2x-1)²
1/(2x-1) to the power of 2
1/2x-1^2
1 divide by (2x-1)^2
Similar expressions
1/(2x+1)^2

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

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

The solution

You have entered [src]

    1     
----------
         2
(2*x - 1)

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

1/((2*x - 1)^2)

Detail solution

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

$- \frac{8 x - 4}{\left(2 x - 1\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       4 - 8*x       
---------------------
         2          2
(2*x - 1) *(2*x - 1)

$$\frac{4 - 8 x}{\left(2 x - 1\right)^{2} \left(2 x - 1\right)^{2}}$$

Simplify

The second derivative [src]

     24    
-----------
          4
(-1 + 2*x)

$$\frac{24}{\left(2 x - 1\right)^{4}}$$

Simplify

The third derivative [src]

   -192    
-----------
          5
(-1 + 2*x)

$$- \frac{192}{\left(2 x - 1\right)^{5}}$$

Simplify

The graph

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