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y=ln^2(3x-2)

Derivative of y=ln^2(3x-2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2         
log (3*x - 2)
$$\log{\left(3 x - 2 \right)}^{2}$$
d /   2         \
--\log (3*x - 2)/
dx               
$$\frac{d}{d x} \log{\left(3 x - 2 \right)}^{2}$$
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. The derivative of is .

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

      1. Differentiate 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: goes to

          So, the result is:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
6*log(3*x - 2)
--------------
   3*x - 2    
$$\frac{6 \log{\left(3 x - 2 \right)}}{3 x - 2}$$
The second derivative [src]
18*(1 - log(-2 + 3*x))
----------------------
               2      
     (-2 + 3*x)       
$$\frac{18 \cdot \left(- \log{\left(3 x - 2 \right)} + 1\right)}{\left(3 x - 2\right)^{2}}$$
The third derivative [src]
54*(-3 + 2*log(-2 + 3*x))
-------------------------
                 3       
       (-2 + 3*x)        
$$\frac{54 \cdot \left(2 \log{\left(3 x - 2 \right)} - 3\right)}{\left(3 x - 2\right)^{3}}$$
The graph
Derivative of y=ln^2(3x-2)