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(log(2*x+1)/log(3))

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Identical expressions
(log(two *x+ one)/log(three))
( logarithm of (2 multiply by x plus 1) divide by logarithm of (3))
( logarithm of (two multiply by x plus one) divide by logarithm of (three))
(log(2x+1)/log(3))
log2x+1/log3
(log(2*x+1) divide by log(3))
Similar expressions
(log(2*x-1)/log(3))

The derivative of the function/ (log(2*x+1)/log(3))

Derivative of (log(2*x+1)/log(3))

The solution

You have entered [src]

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

$$\frac{\log{\left(2 x + 1 \right)}}{\log{\left(3 \right)}}$$

log(2*x + 1)/log(3)

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: $\frac{2}{\left(2 x + 1\right) \log{\left(3 \right)}}$
Now simplify:

$\frac{2}{\left(2 x + 1\right) \log{\left(3 \right)}}$

The answer is:

$\frac{2}{\left(2 x + 1\right) \log{\left(3 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$\frac{2}{\left(2 x + 1\right) \log{\left(3 \right)}}$$

Simplify

The second derivative [src]

       -4        
-----------------
         2       
(1 + 2*x) *log(3)

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of (log(2*x+1)/log(3))