Derivative of sqrt1+sqrtx

You have entered [src]

  ___     ___
\/ 1  + \/ x

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

sqrt(1) + sqrt(x)

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1   
-------
    ___
2*\/ x

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

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