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The derivative of the function/ sqrt(x)-x

Derivative of sqrt(x)-x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  ___    
\/ x  - x
$$\sqrt{x} - x$$ 
sqrt(x) - x
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

    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 answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        1   
-1 + -------
         ___
     2*\/ x
$$-1 + \frac{1}{2 \sqrt{x}}$$
Simplify
The second derivative [src] 
 -1   
------
   3/2
4*x
$$- \frac{1}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
  3   
------
   5/2
8*x
$$\frac{3}{8 x^{\frac{5}{2}}}$$
Simplify
5-я производная [src] 
  105  
-------
    9/2
32*x
$$\frac{105}{32 x^{\frac{9}{2}}}$$
Simplify
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