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3*x-log(x+3)^3

Derivative of 3*x-log(x+3)^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         3       
3*x - log (x + 3)
$$3 x - \log{\left(x + 3 \right)}^{3}$$
d /         3       \
--\3*x - log (x + 3)/
dx                   
$$\frac{d}{d x} \left(3 x - \log{\left(x + 3 \right)}^{3}\right)$$
Detail solution
  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 a constant times a function is the constant times the derivative of the function.

      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:

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
         2       
    3*log (x + 3)
3 - -------------
        x + 3    
$$3 - \frac{3 \log{\left(x + 3 \right)}^{2}}{x + 3}$$
The second derivative [src]
3*(-2 + log(3 + x))*log(3 + x)
------------------------------
                  2           
           (3 + x)            
$$\frac{3 \left(\log{\left(x + 3 \right)} - 2\right) \log{\left(x + 3 \right)}}{\left(x + 3\right)^{2}}$$
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 3*x-log(x+3)^3