Mister Exam

Derivative of ln(3x-4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(3*x - 4)
log(3x4)\log{\left(3 x - 4 \right)}
d               
--(log(3*x - 4))
dx              
ddxlog(3x4)\frac{d}{d x} \log{\left(3 x - 4 \right)}
Detail solution
  1. Let u=3x4u = 3 x - 4.

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

  3. Then, apply the chain rule. Multiply by ddx(3x4)\frac{d}{d x} \left(3 x - 4\right):

    1. Differentiate 3x43 x - 4 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 (1)4\left(-1\right) 4 is zero.

      The result is: 33

    The result of the chain rule is:

    33x4\frac{3}{3 x - 4}

  4. Now simplify:

    33x4\frac{3}{3 x - 4}


The answer is:

33x4\frac{3}{3 x - 4}

The graph
02468-8-6-4-2-1010-10050
The first derivative [src]
   3   
-------
3*x - 4
33x4\frac{3}{3 x - 4}
The second derivative [src]
    -9     
-----------
          2
(-4 + 3*x) 
9(3x4)2- \frac{9}{\left(3 x - 4\right)^{2}}
The third derivative [src]
     54    
-----------
          3
(-4 + 3*x) 
54(3x4)3\frac{54}{\left(3 x - 4\right)^{3}}
The graph
Derivative of ln(3x-4)