Mister Exam

Derivative of ln(1+3x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(1 + 3*x)
$$\log{\left(3 x + 1 \right)}$$
log(1 + 3*x)
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
   3   
-------
1 + 3*x
$$\frac{3}{3 x + 1}$$
The second derivative [src]
   -9     
----------
         2
(1 + 3*x) 
$$- \frac{9}{\left(3 x + 1\right)^{2}}$$
The third derivative [src]
    54    
----------
         3
(1 + 3*x) 
$$\frac{54}{\left(3 x + 1\right)^{3}}$$