Mister Exam

You entered:

sqrt(1+x)/sqrt(1-x)

What you mean?

Derivative of sqrt(1+x)/sqrt(1-x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  _______
\/ 1 + x 
---------
  _______
\/ 1 - x 
$$\frac{\sqrt{x + 1}}{\sqrt{1 - x}}$$
  /  _______\
d |\/ 1 + x |
--|---------|
dx|  _______|
  \\/ 1 - x /
$$\frac{d}{d x} \frac{\sqrt{x + 1}}{\sqrt{1 - x}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. Apply the power rule: goes to

        The result is:

      The result of the chain rule is:

    To find :

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   _______                          
 \/ 1 + x                1          
------------ + ---------------------
         3/2       _______   _______
2*(1 - x)      2*\/ 1 + x *\/ 1 - x 
$$\frac{1}{2 \sqrt{1 - x} \sqrt{x + 1}} + \frac{\sqrt{x + 1}}{2 \left(1 - x\right)^{\frac{3}{2}}}$$
The second derivative [src]
                                       _______
      1                2           3*\/ 1 + x 
- ---------- + ----------------- + -----------
         3/2     _______                    2 
  (1 + x)      \/ 1 + x *(1 - x)     (1 - x)  
----------------------------------------------
                     _______                  
                 4*\/ 1 - x                   
$$\frac{- \frac{1}{\left(x + 1\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - x\right) \sqrt{x + 1}} + \frac{3 \sqrt{x + 1}}{\left(1 - x\right)^{2}}}{4 \sqrt{1 - x}}$$
The third derivative [src]
  /                                                           _______\
  |    1                1                    3            5*\/ 1 + x |
3*|---------- - ------------------ + ------------------ + -----------|
  |       5/2          3/2             _______        2            3 |
  \(1 + x)      (1 + x)   *(1 - x)   \/ 1 + x *(1 - x)      (1 - x)  /
----------------------------------------------------------------------
                                 _______                              
                             8*\/ 1 - x                               
$$\frac{3 \left(\frac{1}{\left(x + 1\right)^{\frac{5}{2}}} - \frac{1}{\left(1 - x\right) \left(x + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x\right)^{2} \sqrt{x + 1}} + \frac{5 \sqrt{x + 1}}{\left(1 - x\right)^{3}}\right)}{8 \sqrt{1 - x}}$$
The graph
Derivative of sqrt(1+x)/sqrt(1-x)