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

Derivative of log(1-t^2)

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

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The solution

You have entered [src] 
   /     2\
log\1 - t /
log⁡(1−t2)\log{\left(1 - t^{2} \right)} 
log(1 - t^2)
Detail solution

  1. Let u=1−t2u = 1 - t^{2}.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddt(1−t2)\frac{d}{d t} \left(1 - t^{2}\right):

    1. Differentiate 1−t21 - t^{2} term by term:

      1. The derivative of the constant 11 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: t2t^{2} goes to 2t2 t

        So, the result is: −2t- 2 t

      The result is: −2t- 2 t

    The result of the chain rule is:

    −2t1−t2- \frac{2 t}{1 - t^{2}}

  4. Now simplify:

    2tt2−1\frac{2 t}{t^{2} - 1}

The answer is:

2tt2−1\frac{2 t}{t^{2} - 1}

The graph
02468-8-6-4-2-1010-2525
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 -2*t 
------
     2
1 - t
−2t1−t2- \frac{2 t}{1 - t^{2}}
Simplify
The second derivative [src] 
  /         2 \
  |      2*t  |
2*|1 - -------|
  |          2|
  \    -1 + t /
---------------
          2    
    -1 + t
2(−2t2t2−1+1)t2−1\frac{2 \left(- \frac{2 t^{2}}{t^{2} - 1} + 1\right)}{t^{2} - 1}
Simplify
The third derivative [src] 
    /          2 \
    |       4*t  |
4*t*|-3 + -------|
    |           2|
    \     -1 + t /
------------------
             2    
    /      2\     
    \-1 + t /
4t(4t2t2−1−3)(t2−1)2\frac{4 t \left(\frac{4 t^{2}}{t^{2} - 1} - 3\right)}{\left(t^{2} - 1\right)^{2}}
Simplify
The graph
Derivative of log(1-t^2)
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