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Derivative of:
Derivative of 2*sin(x)*cos(x)
Derivative of x^(1/4)
Derivative of 9
Derivative of log(sin(x))
Identical expressions
ln^ two (2x- one)
ln squared (2x minus 1)
ln to the power of two (2x minus one)
ln2(2x-1)
ln22x-1
ln²(2x-1)
ln to the power of 2(2x-1)
ln^22x-1
Similar expressions
ln^2(2x+1)

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

Derivative of ln^2(2x-1)

The solution

You have entered [src]

   2         
log (2*x - 1)

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

d /   2         \
--\log (2*x - 1)/
dx

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

Transform

Detail solution

Let $u = \log{\left(2 x - 1 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(2 x - 1 \right)}$ :
1. Let $u = 2 x - 1$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
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 $\left(-1\right) 1$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $\frac{2}{2 x - 1}$
The result of the chain rule is:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

8*(1 - log(-1 + 2*x))
---------------------
               2     
     (-1 + 2*x)

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

Simplify

The third derivative [src]

16*(-3 + 2*log(-1 + 2*x))
-------------------------
                 3       
       (-1 + 2*x)

$$\frac{16 \cdot \left(2 \log{\left(2 x - 1 \right)} - 3\right)}{\left(2 x - 1\right)^{3}}$$

Simplify

The graph

Derivative of ln^2(2x-1)