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

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

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
    -1     
-----------
   ________
  /      2 
\/  1 - x
−11−x2- \frac{1}{\sqrt{1 - x^{2}}} 
-1/sqrt(1 - x^2)
Detail solution

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

    1. Let u=1−x2u = \sqrt{1 - x^{2}}.

    2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

    3. Then, apply the chain rule. Multiply by ddx1−x2\frac{d}{d x} \sqrt{1 - x^{2}}:

      1. Let u=1−x2u = 1 - x^{2}.

      2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

      3. Then, apply the chain rule. Multiply by ddx(1−x2)\frac{d}{d x} \left(1 - x^{2}\right):

        1. Differentiate 1−x21 - x^{2} term by term:

          1. The derivative of the constant 11 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: x2x^{2} goes to 2x2 x

            So, the result is: −2x- 2 x

          The result is: −2x- 2 x

        The result of the chain rule is:

        −x1−x2- \frac{x}{\sqrt{1 - x^{2}}}

      The result of the chain rule is:

      x(1−x2)32\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}

    So, the result is: −x(1−x2)32- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}

The answer is:

−x(1−x2)32- \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}}

The graph
02468-8-6-4-2-1010-2525
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -x     
-----------
        3/2
/     2\   
\1 - x /
−x(1−x2)32- \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 /
3x2x2−1−1(1−x2)32\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 /
3x(5x2x2−1−3)(1−x2)52\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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