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Derivative of:
Derivative of f(x)=x^3
Derivative of (-6)/x^4
Derivative of 5/x^3
Derivative of y=√4-x^2
Identical expressions
y=x*sqrt(one -x^ four)
y equally x multiply by square root of (1 minus x to the power of 4)
y equally x multiply by square root of (one minus x to the power of four)
y=x*√(1-x^4)
y=x*sqrt(1-x4)
y=x*sqrt1-x4
y=x*sqrt(1-x⁴)
y=xsqrt(1-x^4)
y=xsqrt(1-x4)
y=xsqrt1-x4
y=xsqrt1-x^4
Similar expressions
y=x*sqrt(1+x^4)

The derivative of the function/ y=x*sqrt(1-x^4)

Derivative of y=x*sqrt(1-x^4)

The solution

You have entered [src]

     ________
    /      4 
x*\/  1 - x

$$x \sqrt{- x^{4} + 1}$$

  /     ________\
d |    /      4 |
--\x*\/  1 - x  /
dx

$$\frac{d}{d x} x \sqrt{- x^{4} + 1}$$

Transform

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
$g{\left(x \right)} = \sqrt{1 - x^{4}}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = 1 - x^{4}$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - x^{4}\right)$ :
  1. Differentiate $1 - x^{4}$ 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: $x^{4}$ goes to $4 x^{3}$
      So, the result is: $- 4 x^{3}$
    The result is: $- 4 x^{3}$
  The result of the chain rule is:
  
  $- \frac{2 x^{3}}{\sqrt{1 - x^{4}}}$
The result is: $- \frac{2 x^{4}}{\sqrt{1 - x^{4}}} + \sqrt{1 - x^{4}}$
Now simplify:

$\frac{1 - 3 x^{4}}{\sqrt{1 - x^{4}}}$

The answer is:

$\frac{1 - 3 x^{4}}{\sqrt{1 - x^{4}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   ________          4   
  /      4        2*x    
\/  1 - x   - -----------
                 ________
                /      4 
              \/  1 - x

$$- \frac{2 x^{4}}{\sqrt{- x^{4} + 1}} + \sqrt{- x^{4} + 1}$$

Simplify

The second derivative [src]

     /          4 \
   3 |       2*x  |
2*x *|-5 + -------|
     |           4|
     \     -1 + x /
-------------------
       ________    
      /      4     
    \/  1 - x

$$\frac{2 x^{3} \cdot \left(\frac{2 x^{4}}{x^{4} - 1} - 5\right)}{\sqrt{- x^{4} + 1}}$$

Simplify

The third derivative [src]

     /           8           4 \
   2 |        4*x         8*x  |
6*x *|-5 - ---------- + -------|
     |              2         4|
     |     /      4\    -1 + x |
     \     \-1 + x /           /
--------------------------------
             ________           
            /      4            
          \/  1 - x

$$\frac{6 x^{2} \left(- \frac{4 x^{8}}{\left(x^{4} - 1\right)^{2}} + \frac{8 x^{4}}{x^{4} - 1} - 5\right)}{\sqrt{- x^{4} + 1}}$$

Simplify

The graph

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Derivative of y=x*sqrt(1-x^4)

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The solution