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The derivative of the function/ x+2sqrt(x)

Derivative of x+2sqrt(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 + 2*\/ x
2x+x2 \sqrt{x} + x 
x + 2*sqrt(x)
Detail solution

  1. Differentiate 2x+x2 \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: 1x\frac{1}{\sqrt{x}}

    The result is: 1+1x1 + \frac{1}{\sqrt{x}}

The answer is:

1+1x1 + \frac{1}{\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 + -----
      ___
    \/ x
1+1x1 + \frac{1}{\sqrt{x}}
Simplify
The second derivative [src] 
 -1   
------
   3/2
2*x
−12x32- \frac{1}{2 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
  3   
------
   5/2
4*x
34x52\frac{3}{4 x^{\frac{5}{2}}}
Simplify
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