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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:

from to

Piecewise:

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. Apply the power rule: x\sqrt{x} goes to 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
02468-8-6-4-2-1010020
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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