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y=sqrt(6x-x^2)
The derivative of the function/ y=sqrt(6x-x^2)

Derivative of y=sqrt(6x-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   __________
  /        2 
\/  6*x - x
$$\sqrt{- x^{2} + 6 x}$$ 
  /   __________\
d |  /        2 |
--\\/  6*x - x  /
dx
$$\frac{d}{d x} \sqrt{- x^{2} + 6 x}$$
Transform
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 graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    3 - x    
-------------
   __________
  /        2 
\/  6*x - x
$$\frac{- x + 3}{\sqrt{- x^{2} + 6 x}}$$
Simplify
The second derivative [src] 
 /            2\ 
 |    (-3 + x) | 
-|1 + ---------| 
 \    x*(6 - x)/ 
-----------------
    ___________  
  \/ x*(6 - x)
$$- \frac{1 + \frac{\left(x - 3\right)^{2}}{x \left(- x + 6\right)}}{\sqrt{x \left(- x + 6\right)}}$$
Simplify
The third derivative [src] 
   /            2\         
   |    (-3 + x) |         
-3*|1 + ---------|*(-3 + x)
   \    x*(6 - x)/         
---------------------------
                  3/2      
       (x*(6 - x))
$$- \frac{3 \cdot \left(1 + \frac{\left(x - 3\right)^{2}}{x \left(- x + 6\right)}\right) \left(x - 3\right)}{\left(x \left(- x + 6\right)\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of y=sqrt(6x-x^2)
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