Mister Exam

Derivative of ln(3x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(3*x + 1)
log(3x+1)\log{\left(3 x + 1 \right)}
d               
--(log(3*x + 1))
dx              
ddxlog(3x+1)\frac{d}{d x} \log{\left(3 x + 1 \right)}
Detail solution
  1. Let u=3x+1u = 3 x + 1.

  2. The derivative of log(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(3x+1)\frac{d}{d x} \left(3 x + 1\right):

    1. Differentiate 3x+13 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: xx goes to 11

        So, the result is: 33

      2. The derivative of the constant 11 is zero.

      The result is: 33

    The result of the chain rule is:

    33x+1\frac{3}{3 x + 1}

  4. Now simplify:

    33x+1\frac{3}{3 x + 1}


The answer is:

33x+1\frac{3}{3 x + 1}

The graph
02468-8-6-4-2-1010-5050
The first derivative [src]
   3   
-------
3*x + 1
33x+1\frac{3}{3 x + 1}
The second derivative [src]
   -9     
----------
         2
(1 + 3*x) 
9(3x+1)2- \frac{9}{\left(3 x + 1\right)^{2}}
The third derivative [src]
    54    
----------
         3
(1 + 3*x) 
54(3x+1)3\frac{54}{\left(3 x + 1\right)^{3}}
The graph
Derivative of ln(3x+1)