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The derivative of the function/ 1/(1-t^2)

Derivative of 1/(1-t^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1   
------
     2
1 - t
$$\frac{1}{1 - t^{2}}$$ 
1/(1 - t^2)
Detail solution

  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:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   2*t   
---------
        2
/     2\ 
\1 - t /
$$\frac{2 t}{\left(1 - t^{2}\right)^{2}}$$
Simplify
The second derivative [src] 
  /         2 \
  |      4*t  |
2*|1 - -------|
  |          2|
  \    -1 + t /
---------------
            2  
   /      2\   
   \-1 + t /
$$\frac{2 \left(- \frac{4 t^{2}}{t^{2} - 1} + 1\right)}{\left(t^{2} - 1\right)^{2}}$$
Simplify
The third derivative [src] 
     /          2 \
     |       2*t  |
24*t*|-1 + -------|
     |           2|
     \     -1 + t /
-------------------
              3    
     /      2\     
     \-1 + t /
$$\frac{24 t \left(\frac{2 t^{2}}{t^{2} - 1} - 1\right)}{\left(t^{2} - 1\right)^{3}}$$
Simplify
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