Mister Exam

Other calculators

1/sqrt(1-x^2)
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
v

The graph:

from to

Piecewise:

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. 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}}}

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          
--------------------
            ________
/     2\   /      2 
\1 - x /*\/  1 - x
x1−x2(1−x2)\frac{x}{\sqrt{1 - x^{2}} \left(1 - x^{2}\right)}
Simplify
The second derivative [src] 
         2 
      3*x  
 1 + ------
          2
     1 - x 
-----------
        3/2
/     2\   
\1 - x /
3x21−x2+1(1−x2)32\frac{\frac{3 x^{2}}{1 - x^{2}} + 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(5x21−x2+3)(1−x2)52\frac{3 x \left(\frac{5 x^{2}}{1 - x^{2}} + 3\right)}{\left(1 - x^{2}\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of 1/sqrt(1-x^2)
    © Mister Exam – Calculator