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(1+log(x))^3
The derivative of the function/ (1+log(x))^3

Derivative of (1+log(x))^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
            3
(1 + log(x))
$$\left(\log{\left(x \right)} + 1\right)^{3}$$ 
(1 + log(x))^3
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of is .

      The result is:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              2
3*(1 + log(x)) 
---------------
       x
$$\frac{3 \left(\log{\left(x \right)} + 1\right)^{2}}{x}$$
Simplify
The second derivative [src] 
3*(1 - log(x))*(1 + log(x))
---------------------------
              2            
             x
$$\frac{3 \left(1 - \log{\left(x \right)}\right) \left(\log{\left(x \right)} + 1\right)}{x^{2}}$$
Simplify
The third derivative [src] 
  /                 2           \
6*\-2 + (1 + log(x))  - 3*log(x)/
---------------------------------
                 3               
                x
$$\frac{6 \left(\left(\log{\left(x \right)} + 1\right)^{2} - 3 \log{\left(x \right)} - 2\right)}{x^{3}}$$
Simplify
The graph
Derivative of (1+log(x))^3
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