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Derivative of:
Derivative of 4/x^3
Derivative of (x+3)^2*(x+5)-1
Derivative of x^3+2
Derivative of x^(-2)
Integral of d{x}:
1/sqrt(1-x^2)
Limit of the function:
1/sqrt(1-x^2)
Identical expressions
one /sqrt(one -x^ two)
1 divide by square root of (1 minus x squared )
one divide by square root of (one minus x to the power of two)
1/√(1-x^2)
1/sqrt(1-x2)
1/sqrt1-x2
1/sqrt(1-x²)
1/sqrt(1-x to the power of 2)
1/sqrt1-x^2
1 divide by sqrt(1-x^2)
Similar expressions
1/sqrt(1+x^2)

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

Let $u = \sqrt{1 - x^{2}}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
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.
      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:
  
  $- \frac{x}{\sqrt{1 - x^{2}}}$
The result of the chain rule 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          
--------------------
            ________
/     2\   /      2 
\1 - x /*\/  1 - x

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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