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Identical expressions
x*sqrt(sixty-four -x^ two)
x multiply by square root of (64 minus x squared )
x multiply by square root of (sixty minus four minus x to the power of two)
x*√(64-x^2)
x*sqrt(64-x2)
x*sqrt64-x2
x*sqrt(64-x²)
x*sqrt(64-x to the power of 2)
xsqrt(64-x^2)
xsqrt(64-x2)
xsqrt64-x2
xsqrt64-x^2
Similar expressions
x*sqrt(64+x^2)

The derivative of the function/ x*sqrt(64-x^2)

Derivative of x*sqrt(64-x^2)

The solution

You have entered [src]

     _________
    /       2 
x*\/  64 - x

$$x \sqrt{- x^{2} + 64}$$

  /     _________\
d |    /       2 |
--\x*\/  64 - x  /
dx

$$\frac{d}{d x} x \sqrt{- x^{2} + 64}$$

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 $1$
$g{\left(x \right)} = \sqrt{64 - x^{2}}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Let $u = 64 - x^{2}$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(64 - x^{2}\right)$ :
  1. Differentiate $64 - x^{2}$ term by term:
    1. The derivative of the constant $64$ 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:
  
  $- \frac{x}{\sqrt{64 - x^{2}}}$
The result is: $- \frac{x^{2}}{\sqrt{64 - x^{2}}} + \sqrt{64 - x^{2}}$
Now simplify:

$\frac{2 \cdot \left(32 - x^{2}\right)}{\sqrt{64 - x^{2}}}$

The answer is:

$\frac{2 \cdot \left(32 - x^{2}\right)}{\sqrt{64 - x^{2}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   _________         2     
  /       2         x      
\/  64 - x   - ------------
                  _________
                 /       2 
               \/  64 - x

$$- \frac{x^{2}}{\sqrt{- x^{2} + 64}} + \sqrt{- x^{2} + 64}$$

Simplify

The second derivative [src]

  /         2   \
  |        x    |
x*|-3 + --------|
  |            2|
  \     -64 + x /
-----------------
      _________  
     /       2   
   \/  64 - x

$$\frac{x \left(\frac{x^{2}}{x^{2} - 64} - 3\right)}{\sqrt{- x^{2} + 64}}$$

Simplify

The third derivative [src]

  /        2  \ /         2   \
  |       x   | |        x    |
3*|1 + -------|*|-1 + --------|
  |          2| |            2|
  \    64 - x / \     -64 + x /
-------------------------------
             _________         
            /       2          
          \/  64 - x

$$\frac{3 \left(\frac{x^{2}}{- x^{2} + 64} + 1\right) \left(\frac{x^{2}}{x^{2} - 64} - 1\right)}{\sqrt{- x^{2} + 64}}$$

Simplify

3-th derivative [src]

  /        2  \ /         2   \
  |       x   | |        x    |
3*|1 + -------|*|-1 + --------|
  |          2| |            2|
  \    64 - x / \     -64 + x /
-------------------------------
             _________         
            /       2          
          \/  64 - x

$$\frac{3 \left(\frac{x^{2}}{- x^{2} + 64} + 1\right) \left(\frac{x^{2}}{x^{2} - 64} - 1\right)}{\sqrt{- x^{2} + 64}}$$

Simplify

The graph

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Derivative of x*sqrt(64-x^2)

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The solution