Mister Exam

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

Derivative of log*(2x+1)

The solution

You have entered [src]

log(2*x + 1)

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

log(2*x + 1)

Detail solution

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

$\frac{2}{2 x + 1}$
Now simplify:

$\frac{2}{2 x + 1}$

The answer is:

$\frac{2}{2 x + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2   
-------
2*x + 1

$$\frac{2}{2 x + 1}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify