Mister Exam

Derivative of xsqrtx

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
    ___
x*\/ x 
$$\sqrt{x} x$$
d /    ___\
--\x*\/ x /
dx         
$$\frac{d}{d x} \sqrt{x} x$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Apply the power rule: goes to

    The result is:


The answer is:

The graph
The first derivative [src]
    ___
3*\/ x 
-------
   2   
$$\frac{3 \sqrt{x}}{2}$$
The second derivative [src]
   3   
-------
    ___
4*\/ x 
$$\frac{3}{4 \sqrt{x}}$$
The third derivative [src]
 -3   
------
   3/2
8*x   
$$- \frac{3}{8 x^{\frac{3}{2}}}$$
The graph
Derivative of xsqrtx