Mister Exam

Derivative of 1/sqrt(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1  
-----
  ___
\/ x 
$$\frac{1}{\sqrt{x}}$$
1/(sqrt(x))
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Apply the power rule: goes to

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
   -1    
---------
      ___
2*x*\/ x 
$$- \frac{1}{2 \sqrt{x} x}$$
The second derivative [src]
  3   
------
   5/2
4*x   
$$\frac{3}{4 x^{\frac{5}{2}}}$$
The third derivative [src]
 -15  
------
   7/2
8*x   
$$- \frac{15}{8 x^{\frac{7}{2}}}$$
The graph
Derivative of 1/sqrt(x)