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Derivative of 8sqrt(5x+1/5x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
      _____________
     /       x     
8*  /  5*x + - - 1 
  \/         5     
$$8 \sqrt{\left(\frac{x}{5} + 5 x\right) - 1}$$
8*sqrt(5*x + x/5 - 1)
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        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:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
        104        
-------------------
      _____________
     /       x     
5*  /  5*x + - - 1 
  \/         5     
$$\frac{104}{5 \sqrt{\left(\frac{x}{5} + 5 x\right) - 1}}$$
The second derivative [src]
      -1352      
-----------------
              3/2
   /     26*x\   
25*|-1 + ----|   
   \      5  /   
$$- \frac{1352}{25 \left(\frac{26 x}{5} - 1\right)^{\frac{3}{2}}}$$
The third derivative [src]
      52728       
------------------
               5/2
    /     26*x\   
125*|-1 + ----|   
    \      5  /   
$$\frac{52728}{125 \left(\frac{26 x}{5} - 1\right)^{\frac{5}{2}}}$$