Mister Exam

Derivative of ln(3x^3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /   3\
log\3*x /
log(3x3)\log{\left(3 x^{3} \right)}
log(3*x^3)
Detail solution
  1. Let u=3x3u = 3 x^{3}.

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

  3. Then, apply the chain rule. Multiply by ddx3x3\frac{d}{d x} 3 x^{3}:

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

      1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

      So, the result is: 9x29 x^{2}

    The result of the chain rule is:

    3x\frac{3}{x}


The answer is:

3x\frac{3}{x}

The graph
02468-8-6-4-2-1010-5050
The first derivative [src]
3
-
x
3x\frac{3}{x}
The second derivative [src]
-3 
---
  2
 x 
3x2- \frac{3}{x^{2}}
The third derivative [src]
6 
--
 3
x 
6x3\frac{6}{x^{3}}