Mister Exam

# Derivative of 1/sqrt(1-x²)

Function f() - derivative -N order at the point
v

from to

### The solution

You have entered [src]
       1
1*-----------
________
/      2
\/  1 - x  
$$1 \cdot \frac{1}{\sqrt{- x^{2} + 1}}$$
d /       1     \
--|1*-----------|
dx|     ________|
|    /      2 |
\  \/  1 - x  /
$$\frac{d}{d x} 1 \cdot \frac{1}{\sqrt{- x^{2} + 1}}$$
Detail solution
1. Apply the quotient rule, which is:

and .

To find :

1. The derivative of the constant is zero.

To find :

1. Let .

2. Apply the power rule: goes to

3. Then, apply the chain rule. Multiply by :

1. Differentiate term by term:

1. The derivative of the constant 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: goes to

So, the result is:

The result is:

The result of the chain rule is:

Now plug in to the quotient rule:

The graph
The first derivative [src]
         x
--------------------
________
/     2\   /      2
\1 - x /*\/  1 - x  
$$\frac{x}{\sqrt{- x^{2} + 1} \cdot \left(- x^{2} + 1\right)}$$
The second derivative [src]
 /          2 \
|       3*x  |
-|-1 + -------|
|           2|
\     -1 + x /
----------------
3/2
/     2\
\1 - x /      
$$- \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}$$
The third derivative [src]
     /          2 \
|       5*x  |
-3*x*|-3 + -------|
|           2|
\     -1 + x /
-------------------
5/2
/     2\
\1 - x /       
$$- \frac{3 x \left(\frac{5 x^{2}}{x^{2} - 1} - 3\right)}{\left(- x^{2} + 1\right)^{\frac{5}{2}}}$$
The graph