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Integral of d{x}:
sqrt(1-x^3)
Identical expressions
y=sqrt(one -x^ three)
y equally square root of (1 minus x cubed )
y equally square root of (one minus x to the power of three)
y=√(1-x^3)
y=sqrt(1-x3)
y=sqrt1-x3
y=sqrt(1-x³)
y=sqrt(1-x to the power of 3)
y=sqrt1-x^3
Similar expressions
y=sqrt(1+x^3)

The derivative of the function/ y=sqrt(1-x^3)

Derivative of y=sqrt(1-x^3)

The solution

You have entered [src]

   ________
  /      3 
\/  1 - x

$$\sqrt{1 - x^{3}}$$

sqrt(1 - x^3)

Detail solution

Let $u = 1 - x^{3}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - x^{3}\right)$ :
1. Differentiate $1 - x^{3}$ 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: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $- 3 x^{2}$
  The result is: $- 3 x^{2}$
The result of the chain rule is:

$- \frac{3 x^{2}}{2 \sqrt{1 - x^{3}}}$

The answer is:

$- \frac{3 x^{2}}{2 \sqrt{1 - x^{3}}}$

The graph

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Plot the graph f'(x)

The first derivative [src]

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

$$- \frac{3 x^{2}}{2 \sqrt{1 - x^{3}}}$$

Simplify

The second derivative [src]

     /          3   \
     |       3*x    |
-3*x*|1 + ----------|
     |      /     3\|
     \    4*\1 - x //
---------------------
        ________     
       /      3      
     \/  1 - x

$$- \frac{3 x \left(\frac{3 x^{3}}{4 \left(1 - x^{3}\right)} + 1\right)}{\sqrt{1 - x^{3}}}$$

Simplify

The third derivative [src]

   /          3             6   \
   |       9*x          27*x    |
-3*|1 + ---------- + -----------|
   |      /     3\             2|
   |    2*\1 - x /     /     3\ |
   \                 8*\1 - x / /
---------------------------------
              ________           
             /      3            
           \/  1 - x

$$- \frac{3 \left(\frac{27 x^{6}}{8 \left(1 - x^{3}\right)^{2}} + \frac{9 x^{3}}{2 \left(1 - x^{3}\right)} + 1\right)}{\sqrt{1 - x^{3}}}$$

Simplify

The graph

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Derivative of y=sqrt(1-x^3)

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The solution