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

Derivative of lg^2(x+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2       
log (x + 3)
$$\log{\left(x + 3 \right)}^{2}$$ 
log(x + 3)^2
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
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
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