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Derivative of log(x+3)^3
Identical expressions
log(x+ three)^ three
logarithm of (x plus 3) cubed
logarithm of (x plus three) to the power of three
log(x+3)3
logx+33
log(x+3)³
log(x+3) to the power of 3
logx+3^3
Similar expressions
log(x-3)^3

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

Derivative of log(x+3)^3

The solution

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   3       
log (x + 3)

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

log(x + 3)^3

Detail solution

Let $u = \log{\left(x + 3 \right)}$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
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:
    1. Apply the power rule: $x$ goes to $1$
    2. 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:

$\frac{3 \log{\left(x + 3 \right)}^{2}}{x + 3}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

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 log(x+3)^3

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The solution