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Derivative of 2/3x*sqrtx-3x+1

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
2*x   ___          
---*\/ x  - 3*x + 1
 3                 
$$\left(\sqrt{x} \frac{2 x}{3} - 3 x\right) + 1$$
(2*x/3)*sqrt(x) - 3*x + 1
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

      1. Apply the quotient rule, which is:

        and .

        To find :

        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:

        To find :

        1. The derivative of the constant is zero.

        Now plug in to the quotient rule:

      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 answer is:

The graph
The first derivative [src]
       ___
-3 + \/ x 
$$\sqrt{x} - 3$$
The second derivative [src]
   1   
-------
    ___
2*\/ x 
$$\frac{1}{2 \sqrt{x}}$$
The third derivative [src]
 -1   
------
   3/2
4*x   
$$- \frac{1}{4 x^{\frac{3}{2}}}$$