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Derivative of:
Derivative of cos(5-3*x)
Derivative of cos^3(t)
Derivative of asin(y^2)
Derivative of (5x^2+2)×(x^2-4)^3
Identical expressions
(log(two *x- one))/ eight
( logarithm of (2 multiply by x minus 1)) divide by 8
( logarithm of (two multiply by x minus one)) divide by eight
(log(2x-1))/8
log2x-1/8
(log(2*x-1)) divide by 8
Similar expressions
(log(2*x+1))/8

The derivative of the function/ (log(2*x-1))/8

Derivative of (log(2*x-1))/8

The solution

You have entered [src]

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

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

log(2*x - 1)/8

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
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 $-1$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $\frac{2}{2 x - 1}$
So, the result is: $\frac{1}{4 \left(2 x - 1\right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

4-я производная [src]

    -12    
-----------
          4
(-1 + 2*x)

$$- \frac{12}{\left(2 x - 1\right)^{4}}$$

Simplify