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

Derivative of log(2*x-1,2)

The solution

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log(2*x - 6/5)

$$\log{\left(2 x - \frac{6}{5} \right)}$$

log(2*x - 6/5)

Detail solution

Let $u = 2 x - \frac{6}{5}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - \frac{6}{5}\right)$ :
1. Differentiate $2 x - \frac{6}{5}$ 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 $- \frac{6}{5}$ is zero.
  The result is: $2$
The result of the chain rule is:

$\frac{2}{2 x - \frac{6}{5}}$
Now simplify:

$\frac{5}{5 x - 3}$

The answer is:

$\frac{5}{5 x - 3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2    
---------
2*x - 6/5

$$\frac{2}{2 x - \frac{6}{5}}$$

Simplify

The second derivative [src]

    -1     
-----------
          2
(-3/5 + x)

$$- \frac{1}{\left(x - \frac{3}{5}\right)^{2}}$$

Simplify

The third derivative [src]

     2     
-----------
          3
(-3/5 + x)

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

Simplify