Derivative of x+sqrt(x)

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x + \/ x

$$\sqrt{x} + x$$

x + sqrt(x)

Detail solution

Differentiate $\sqrt{x} + x$ term by term:
1. Apply the power rule: $x$ goes to $1$
2. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
The result is: $1 + \frac{1}{2 \sqrt{x}}$

The answer is:

$1 + \frac{1}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       1   
1 + -------
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    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

The graph