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ln(x+3)^3

Derivative of ln(x+3)^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3       
log (x + 3)
$$\log{\left(x + 3 \right)}^{3}$$
d /   3       \
--\log (x + 3)/
dx             
$$\frac{d}{d x} \log{\left(x + 3 \right)}^{3}$$
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. Apply the power rule: goes to

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