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Similar expressions
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The derivative of the function/ -1/(sqrt(1-x^2))

Derivative of -1/(sqrt(1-x^2))

The solution

You have entered [src]

    -1     
-----------
   ________
  /      2 
\/  1 - x

$$- \frac{1}{\sqrt{1 - x^{2}}}$$

-1/sqrt(1 - x^2)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{1 - x^{2}}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{1 - x^{2}}$ :
  1. Let $u = 1 - x^{2}$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  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.
        
        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:
    
    $- \frac{x}{\sqrt{1 - x^{2}}}$
  The result of the chain rule is:
  
  $\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$
So, the result is: $- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -x     
-----------
        3/2
/     2\   
\1 - x /

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

Simplify

The second derivative [src]

          2 
       3*x  
-1 + -------
           2
     -1 + x 
------------
        3/2 
/     2\    
\1 - x /

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

Simplify

The third derivative [src]

    /          2 \
    |       5*x  |
3*x*|-3 + -------|
    |           2|
    \     -1 + x /
------------------
           5/2    
   /     2\       
   \1 - x /

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

Simplify

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Derivative of -1/(sqrt(1-x^2))

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The solution