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Integral of d{x}:
sqrt(4-x^2)/x
Graphing y =:
sqrt(4-x^2)/x
Limit of the function:
sqrt(4-x^2)/x
Identical expressions
sqrt(four -x^ two)/x
square root of (4 minus x squared ) divide by x
square root of (four minus x to the power of two) divide by x
√(4-x^2)/x
sqrt(4-x2)/x
sqrt4-x2/x
sqrt(4-x²)/x
sqrt(4-x to the power of 2)/x
sqrt4-x^2/x
sqrt(4-x^2) divide by x
Similar expressions
sqrt(4+x^2)/x

The derivative of the function/ sqrt(4-x^2)/x

Derivative of sqrt(4-x^2)/x

The solution

You have entered [src]

   ________
  /      2 
\/  4 - x  
-----------
     x

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

sqrt(4 - x^2)/x

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = \sqrt{4 - x^{2}}$ and $g{\left(x \right)} = x$ .

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

$\frac{- \frac{x^{2}}{\sqrt{4 - x^{2}}} - \sqrt{4 - x^{2}}}{x^{2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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Derivative of sqrt(4-x^2)/x

The graph:

Piecewise:

The solution