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x*sqrt(x)^2-x+1

Derivative of x*sqrt(x)^2-x+1

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

The graph:

from to

Piecewise:

The solution

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

    1. Differentiate term by term:

      1. Apply the product rule:

        ; to find :

        1. Apply the power rule: goes to

        ; to find :

        1. Let .

        2. Apply the power rule: goes to

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

          1. Apply the power rule: goes to

          The result of the chain rule is:

        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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
              2
           ___ 
-1 + x + \/ x  
$$\left(\sqrt{x}\right)^{2} + x - 1$$
The second derivative [src]
2
$$2$$
The third derivative [src]
0
$$0$$
The graph
Derivative of x*sqrt(x)^2-x+1