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The derivative of the function/ log3(4-x^2)

Derivative of log3(4-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /     2\
log\4 - x /
-----------
   log(3)
$$\frac{\log{\left(4 - x^{2} \right)}}{\log{\left(3 \right)}}$$ 
log(4 - x^2)/log(3)
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. The derivative of the constant is zero.

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

          1. Apply the power rule: goes to

          So, the result is:

        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] 
      -2*x     
---------------
/     2\       
\4 - x /*log(3)
$$- \frac{2 x}{\left(4 - x^{2}\right) \log{\left(3 \right)}}$$
Simplify
The second derivative [src] 
   /          2 \
   |       2*x  |
-2*|-1 + -------|
   |           2|
   \     -4 + x /
-----------------
 /      2\       
 \-4 + x /*log(3)
$$- \frac{2 \left(\frac{2 x^{2}}{x^{2} - 4} - 1\right)}{\left(x^{2} - 4\right) \log{\left(3 \right)}}$$
Simplify
The third derivative [src] 
    /          2 \
    |       4*x  |
4*x*|-3 + -------|
    |           2|
    \     -4 + x /
------------------
         2        
/      2\         
\-4 + x / *log(3)
$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 4} - 3\right)}{\left(x^{2} - 4\right)^{2} \log{\left(3 \right)}}$$
Simplify
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