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

Derivative of x-sqrt(x)

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

The graph:

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The solution

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

  1. Differentiate −x+x- \sqrt{x} + x term by term:

    1. Apply the power rule: xx goes to 11

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

      So, the result is: −12x- \frac{1}{2 \sqrt{x}}

    The result is: 1−12x1 - \frac{1}{2 \sqrt{x}}

The answer is:

1−12x1 - \frac{1}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       1   
1 - -------
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    2*\/ x
1−12x1 - \frac{1}{2 \sqrt{x}}
Simplify
The second derivative [src] 
  1   
------
   3/2
4*x
14x32\frac{1}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
 -3   
------
   5/2
8*x
−38x52- \frac{3}{8 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of x-sqrt(x)
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