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z=sqrt(x-x^3)
The derivative of the function/ z=sqrt(x-x^3)

Derivative of z=sqrt(x-x^3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
  /      3 
\/  x - x
$$\sqrt{- x^{3} + x}$$ 
  /   ________\
d |  /      3 |
--\\/  x - x  /
dx
$$\frac{d}{d x} \sqrt{- x^{3} + x}$$
Transform
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. Apply the power rule: goes to

      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] 
         2 
  1   3*x  
  - - ---- 
  2    2   
-----------
   ________
  /      3 
\/  x - x
$$\frac{- \frac{3 x^{2}}{2} + \frac{1}{2}}{\sqrt{- x^{3} + x}}$$
Simplify
The second derivative [src] 
 /                 2\ 
 |      /        2\ | 
 |      \-1 + 3*x / | 
-|3*x + ------------| 
 |          /     2\| 
 \      4*x*\1 - x // 
----------------------
      ____________    
     /   /     2\     
   \/  x*\1 - x /
$$- \frac{3 x + \frac{\left(3 x^{2} - 1\right)^{2}}{4 x \left(- x^{2} + 1\right)}}{\sqrt{x \left(- x^{2} + 1\right)}}$$
Simplify
The third derivative [src] 
   /                                3 \
   |      /        2\    /        2\  |
   |    3*\-1 + 3*x /    \-1 + 3*x /  |
-3*|1 + ------------- + --------------|
   |        /     2\                 2|
   |      2*\1 - x /       2 /     2\ |
   \                    8*x *\1 - x / /
---------------------------------------
               ____________            
              /   /     2\             
            \/  x*\1 - x /
$$- \frac{3 \cdot \left(1 + \frac{3 \cdot \left(3 x^{2} - 1\right)}{2 \cdot \left(- x^{2} + 1\right)} + \frac{\left(3 x^{2} - 1\right)^{3}}{8 x^{2} \left(- x^{2} + 1\right)^{2}}\right)}{\sqrt{x \left(- x^{2} + 1\right)}}$$
Simplify
The graph
Derivative of z=sqrt(x-x^3)
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