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Derivative of:
Derivative of (x+3)^3
Derivative of ln(x)^2
Derivative of sqrt(1/x)
Derivative of ln(1/x)
Identical expressions
lg^ two (x+ three)
lg squared (x plus 3)
lg to the power of two (x plus three)
lg2(x+3)
lg2x+3
lg²(x+3)
lg to the power of 2(x+3)
lg^2x+3
Similar expressions
lg^2(x-3)

The derivative of the function/ lg^2(x+3)

Derivative of lg^2(x+3)

The solution

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   2       
log (x + 3)

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

log(x + 3)^2

Detail solution

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

2*(1 - log(3 + x))
------------------
            2     
     (3 + x)

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

Simplify

The third derivative [src]

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

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

Simplify