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y=ln^4(3x+1)
The derivative of the function/ y=ln^4(3x+1)

Derivative of y=ln^4(3x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   4         
log (3*x + 1)
$$\log{\left(3 x + 1 \right)}^{4}$$ 
log(3*x + 1)^4
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      3         
12*log (3*x + 1)
----------------
    3*x + 1
$$\frac{12 \log{\left(3 x + 1 \right)}^{3}}{3 x + 1}$$
Simplify
The second derivative [src] 
      2                            
36*log (1 + 3*x)*(3 - log(1 + 3*x))
-----------------------------------
                      2            
             (1 + 3*x)
$$\frac{36 \left(3 - \log{\left(3 x + 1 \right)}\right) \log{\left(3 x + 1 \right)}^{2}}{\left(3 x + 1\right)^{2}}$$
Simplify
The third derivative [src] 
    /                          2         \             
108*\6 - 9*log(1 + 3*x) + 2*log (1 + 3*x)/*log(1 + 3*x)
-------------------------------------------------------
                                3                      
                       (1 + 3*x)
$$\frac{108 \left(2 \log{\left(3 x + 1 \right)}^{2} - 9 \log{\left(3 x + 1 \right)} + 6\right) \log{\left(3 x + 1 \right)}}{\left(3 x + 1\right)^{3}}$$
Simplify
The graph
Derivative of y=ln^4(3x+1)
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