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Equation:
ln(4-x^2)
Identical expressions
ln(four -x^ two)
ln(4 minus x squared )
ln(four minus x to the power of two)
ln(4-x2)
ln4-x2
ln(4-x²)
ln(4-x to the power of 2)
ln4-x^2
Similar expressions
ln(4+x^2)

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

Derivative of ln(4-x^2)

The solution

You have entered [src]

   /     2\
log\4 - x /

$$\log{\left(4 - x^{2} \right)}$$

log(4 - x^2)

Detail solution

Let $u = 4 - x^{2}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 - x^{2}\right)$ :
1. Differentiate $4 - x^{2}$ term by term:
  1. The derivative of the constant $4$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $- 2 x$
  The result is: $- 2 x$
The result of the chain rule is:

$- \frac{2 x}{4 - x^{2}}$
Now simplify:

$\frac{2 x}{x^{2} - 4}$

The answer is:

$\frac{2 x}{x^{2} - 4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 -2*x 
------
     2
4 - x

$$- \frac{2 x}{4 - x^{2}}$$

Simplify

The second derivative [src]

  /         2 \
  |      2*x  |
2*|1 - -------|
  |          2|
  \    -4 + x /
---------------
          2    
    -4 + x

$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} - 4} + 1\right)}{x^{2} - 4}$$

Simplify

4-я производная [src]

   /           4           2 \
   |        8*x         8*x  |
12*|-1 - ---------- + -------|
   |              2         2|
   |     /      2\    -4 + x |
   \     \-4 + x /           /
------------------------------
                   2          
          /      2\           
          \-4 + x /

$$\frac{12 \left(- \frac{8 x^{4}}{\left(x^{2} - 4\right)^{2}} + \frac{8 x^{2}}{x^{2} - 4} - 1\right)}{\left(x^{2} - 4\right)^{2}}$$

Simplify

The third derivative [src]

    /          2 \
    |       4*x  |
4*x*|-3 + -------|
    |           2|
    \     -4 + x /
------------------
             2    
    /      2\     
    \-4 + x /

$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 4} - 3\right)}{\left(x^{2} - 4\right)^{2}}$$

Simplify

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Derivative of ln(4-x^2)

The graph:

Piecewise:

The solution