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The derivative of the function/ log4(x+3)

Derivative of log4(x+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x + 3)
----------
  log(4)
$$\frac{\log{\left(x + 3 \right)}}{\log{\left(4 \right)}}$$ 
log(x + 3)/log(4)
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      1       
--------------
(x + 3)*log(4)
$$\frac{1}{\left(x + 3\right) \log{\left(4 \right)}}$$
Simplify
The second derivative [src] 
      -1       
---------------
       2       
(3 + x) *log(4)
$$- \frac{1}{\left(x + 3\right)^{2} \log{\left(4 \right)}}$$
Simplify
The third derivative [src] 
       2       
---------------
       3       
(3 + x) *log(4)
$$\frac{2}{\left(x + 3\right)^{3} \log{\left(4 \right)}}$$
Simplify
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