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Identical expressions
log(one -x^ two)/log(five)
logarithm of (1 minus x squared ) divide by logarithm of (5)
logarithm of (one minus x to the power of two) divide by logarithm of (five)
log(1-x2)/log(5)
log1-x2/log5
log(1-x²)/log(5)
log(1-x to the power of 2)/log(5)
log1-x^2/log5
log(1-x^2) divide by log(5)
Similar expressions
log(1+x^2)/log(5)

The derivative of the function/ log(1-x^2)/log(5)

Derivative of log(1-x^2)/log(5)

The solution

You have entered [src]

   /     2\
log\1 - x /
-----------
   log(5)

$$\frac{\log{\left(1 - x^{2} \right)}}{\log{\left(5 \right)}}$$

log(1 - x^2)/log(5)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 1 - x^{2}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - x^{2}\right)$ :
  1. Differentiate $1 - x^{2}$ term by term:
    1. The derivative of the constant $1$ 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:
  
  $- \frac{2 x}{1 - x^{2}}$
So, the result is: $- \frac{2 x}{\left(1 - x^{2}\right) \log{\left(5 \right)}}$
Now simplify:

$\frac{2 x}{\left(x^{2} - 1\right) \log{\left(5 \right)}}$

The answer is:

$\frac{2 x}{\left(x^{2} - 1\right) \log{\left(5 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      -2*x     
---------------
/     2\       
\1 - x /*log(5)

$$- \frac{2 x}{\left(1 - x^{2}\right) \log{\left(5 \right)}}$$

Simplify

The second derivative [src]

   /          2 \
   |       2*x  |
-2*|-1 + -------|
   |           2|
   \     -1 + x /
-----------------
 /      2\       
 \-1 + x /*log(5)

$$- \frac{2 \left(\frac{2 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right) \log{\left(5 \right)}}$$

Simplify

The third derivative [src]

    /          2 \
    |       4*x  |
4*x*|-3 + -------|
    |           2|
    \     -1 + x /
------------------
         2        
/      2\         
\-1 + x / *log(5)

$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{2} \log{\left(5 \right)}}$$

Simplify

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Derivative of log(1-x^2)/log(5)

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The solution