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

Derivative of sqrt(1-x^2)

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

The graph:

from to

Piecewise:

The solution

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

  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:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -x     
-----------
   ________
  /      2 
\/  1 - x
$$- \frac{x}{\sqrt{1 - x^{2}}}$$
Simplify
The second derivative [src] 
 /       2  \ 
 |      x   | 
-|1 + ------| 
 |         2| 
 \    1 - x / 
--------------
    ________  
   /      2   
 \/  1 - x
$$- \frac{\frac{x^{2}}{1 - x^{2}} + 1}{\sqrt{1 - x^{2}}}$$
Simplify
The third derivative [src] 
     /       2  \
     |      x   |
-3*x*|1 + ------|
     |         2|
     \    1 - x /
-----------------
           3/2   
   /     2\      
   \1 - x /
$$- \frac{3 x \left(\frac{x^{2}}{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(1-x^2)
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