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The derivative of the function/ sqrt(6x-15x^2)

Derivative of sqrt(6x-15x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   _____________
  /           2 
\/  6*x - 15*x
$$\sqrt{- 15 x^{2} + 6 x}$$ 
sqrt(6*x - 15*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 graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    3 - 15*x    
----------------
   _____________
  /           2 
\/  6*x - 15*x
$$\frac{3 - 15 x}{\sqrt{- 15 x^{2} + 6 x}}$$
Simplify
The second derivative [src] 
       /              2\ 
   ___ |    (-1 + 5*x) | 
-\/ 3 *|5 + -----------| 
       \    x*(2 - 5*x)/ 
-------------------------
       _____________     
     \/ x*(2 - 5*x)
$$- \frac{\sqrt{3} \left(5 + \frac{\left(5 x - 1\right)^{2}}{x \left(2 - 5 x\right)}\right)}{\sqrt{x \left(2 - 5 x\right)}}$$
Simplify
The third derivative [src] 
                    /              2\
     ___            |    (-1 + 5*x) |
-3*\/ 3 *(-1 + 5*x)*|5 + -----------|
                    \    x*(2 - 5*x)/
-------------------------------------
                        3/2          
           (x*(2 - 5*x))
$$- \frac{3 \sqrt{3} \left(5 + \frac{\left(5 x - 1\right)^{2}}{x \left(2 - 5 x\right)}\right) \left(5 x - 1\right)}{\left(x \left(2 - 5 x\right)\right)^{\frac{3}{2}}}$$
Simplify
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