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The derivative of the function/ y=sqrt*(2ax-x^2)

Derivative of y=sqrt*(2ax-x^2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ____________
  /          2 
\/  2*a*x - x
$$\sqrt{2 a x - x^{2}}$$ 
sqrt((2*a)*x - x^2)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The first derivative [src] 
     a - x     
---------------
   ____________
  /          2 
\/  2*a*x - x
$$\frac{a - x}{\sqrt{2 a x - x^{2}}}$$
Simplify
The second derivative [src] 
 /             2  \ 
 |      (a - x)   | 
-|1 + ------------| 
 \    x*(-x + 2*a)/ 
--------------------
    ______________  
  \/ x*(-x + 2*a)
$$- \frac{1 + \frac{\left(a - x\right)^{2}}{x \left(2 a - x\right)}}{\sqrt{x \left(2 a - x\right)}}$$
Simplify
The third derivative [src] 
  /             2  \        
  |      (a - x)   |        
3*|1 + ------------|*(a - x)
  \    x*(-x + 2*a)/        
----------------------------
                   3/2      
     (x*(-x + 2*a))
$$\frac{3 \left(1 + \frac{\left(a - x\right)^{2}}{x \left(2 a - x\right)}\right) \left(a - x\right)}{\left(x \left(2 a - x\right)\right)^{\frac{3}{2}}}$$
Simplify
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