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Graphing y =:
3*x-log(x+3)^3
Identical expressions
three *x-log(x+ three)^ three
3 multiply by x minus logarithm of (x plus 3) cubed
three multiply by x minus logarithm of (x plus three) to the power of three
3*x-log(x+3)3
3*x-logx+33
3*x-log(x+3)³
3*x-log(x+3) to the power of 3
3x-log(x+3)^3
3x-log(x+3)3
3x-logx+33
3x-logx+3^3
Similar expressions
3*x-log(x-3)^3
3*x+log(x+3)^3

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

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

The solution

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         3       
3*x - log (x + 3)

$$3 x - \log{\left(x + 3 \right)}^{3}$$

d /         3       \
--\3*x - log (x + 3)/
dx

$$\frac{d}{d x} \left(3 x - \log{\left(x + 3 \right)}^{3}\right)$$

Transform

Detail solution

Differentiate $3 x - \log{\left(x + 3 \right)}^{3}$ 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: $x$ goes to $1$
  So, the result is: $3$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \log{\left(x + 3 \right)}$ .
  2. Apply the power rule: $u^{3}$ goes to $3 u^{2}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x + 3 \right)}$ :
    1. Let $u = x + 3$ .
    2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 3\right)$ :
      1. Differentiate $x + 3$ term by term:
        
        Apply the power rule: $x$ goes to $1$
        
        The derivative of the constant $3$ is zero.
        
        The result is: $1$
      The result of the chain rule is:
      
      $\frac{1}{x + 3}$
    The result of the chain rule is:
    
    $\frac{3 \log{\left(x + 3 \right)}^{2}}{x + 3}$
  So, the result is: $- \frac{3 \log{\left(x + 3 \right)}^{2}}{x + 3}$
The result is: $3 - \frac{3 \log{\left(x + 3 \right)}^{2}}{x + 3}$
Now simplify:

$\frac{3 \left(x - \log{\left(x + 3 \right)}^{2} + 3\right)}{x + 3}$

The answer is:

$\frac{3 \left(x - \log{\left(x + 3 \right)}^{2} + 3\right)}{x + 3}$

The graph

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The first derivative [src]

         2       
    3*log (x + 3)
3 - -------------
        x + 3

$$3 - \frac{3 \log{\left(x + 3 \right)}^{2}}{x + 3}$$

Simplify

The second derivative [src]

3*(-2 + log(3 + x))*log(3 + x)
------------------------------
                  2           
           (3 + x)

$$\frac{3 \left(\log{\left(x + 3 \right)} - 2\right) \log{\left(x + 3 \right)}}{\left(x + 3\right)^{2}}$$

Simplify

The third derivative [src]

  /        2                      \
6*\-1 - log (3 + x) + 3*log(3 + x)/
-----------------------------------
                     3             
              (3 + x)

$$\frac{6 \left(- \log{\left(x + 3 \right)}^{2} + 3 \log{\left(x + 3 \right)} - 1\right)}{\left(x + 3\right)^{3}}$$

Simplify

The graph

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

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