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√x+√x+√x
The derivative of the function/ √x+√x+√x

Derivative of √x+√x+√x

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
  ___     ___     ___
\/ x  + \/ x  + \/ x
x+(x+x)\sqrt{x} + \left(\sqrt{x} + \sqrt{x}\right) 
sqrt(x) + sqrt(x) + sqrt(x)
Detail solution

  1. Differentiate x+(x+x)\sqrt{x} + \left(\sqrt{x} + \sqrt{x}\right) term by term:

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

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

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

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

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

    The result is: 32x\frac{3}{2 \sqrt{x}}

The answer is:

32x\frac{3}{2 \sqrt{x}}

The graph
02468-8-6-4-2-1010010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   3   
-------
    ___
2*\/ x
32x\frac{3}{2 \sqrt{x}}
Simplify
The second derivative [src] 
 -3   
------
   3/2
4*x
−34x32- \frac{3}{4 x^{\frac{3}{2}}}
Simplify
The third derivative [src] 
  9   
------
   5/2
8*x
98x52\frac{9}{8 x^{\frac{5}{2}}}
Simplify
The graph
Derivative of √x+√x+√x
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