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Derivative of:
Derivative of y=4x+5
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Derivative of x^-tan(x)
Derivative of (x-1)√x^2-2x+2
Identical expressions
sqrt(four -(x- two a)^2)
square root of (4 minus (x minus 2a) squared )
square root of (four minus (x minus two a) squared )
√(4-(x-2a)^2)
sqrt(4-(x-2a)2)
sqrt4-x-2a2
sqrt(4-(x-2a)²)
sqrt(4-(x-2a) to the power of 2)
sqrt4-x-2a^2
Similar expressions
sqrt(4-(x+2a)^2)
sqrt(4+(x-2a)^2)

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

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

The solution

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   ________________
  /              2 
\/  4 - (x - 2*a)

$$\sqrt{4 - \left(- 2 a + x\right)^{2}}$$

sqrt(4 - (x - 2*a)^2)

Detail solution

Let $u = 4 - \left(- 2 a + x\right)^{2}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} \left(4 - \left(- 2 a + x\right)^{2}\right)$ :
1. Differentiate $4 - \left(- 2 a + x\right)^{2}$ 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. Let $u = - 2 a + x$ .
    2. Apply the power rule: $u^{2}$ goes to $2 u$
    3. Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} \left(- 2 a + x\right)$ :
      1. Differentiate $- 2 a + x$ term by term:
        
        Apply the power rule: $x$ goes to $1$
        
        The derivative of the constant $- 2 a$ is zero.
        
        The result is: $1$
      The result of the chain rule is:
      
      $- 4 a + 2 x$
    So, the result is: $4 a - 2 x$
  The result is: $4 a - 2 x$
The result of the chain rule is:

$\frac{4 a - 2 x}{2 \sqrt{4 - \left(- 2 a + x\right)^{2}}}$
Now simplify:

$\frac{2 a - x}{\sqrt{4 - \left(- 2 a + x\right)^{2}}}$

The answer is:

$\frac{2 a - x}{\sqrt{4 - \left(- 2 a + x\right)^{2}}}$

The first derivative [src]

      -x + 2*a     
-------------------
   ________________
  /              2 
\/  4 - (x - 2*a)

$$\frac{2 a - x}{\sqrt{4 - \left(- 2 a + x\right)^{2}}}$$

Simplify

The second derivative [src]

 /               2  \ 
 |     (-x + 2*a)   | 
-|1 + --------------| 
 |                 2| 
 \    4 - (x - 2*a) / 
----------------------
    ________________  
   /              2   
 \/  4 - (x - 2*a)

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

Simplify

The third derivative [src]

  /               2  \           
  |     (-x + 2*a)   |           
3*|1 + --------------|*(-x + 2*a)
  |                 2|           
  \    4 - (x - 2*a) /           
---------------------------------
                       3/2       
       /             2\          
       \4 - (x - 2*a) /

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

Simplify

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

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