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Derivative of lnsqrt(sin2x/1-sin2x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /    _____________________\
   |   / sin(2*x)            |
log|  /  -------- - sin(2*x) |
   \\/      1                /
$$\log{\left(\sqrt{- \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{1}} \right)}$$
log(sqrt(sin(2*x)/1 - sin(2*x)))
Detail solution
  1. Let .

  2. The derivative of is .

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

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

          1. Let .

          2. The derivative of sine is cosine:

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

            1. 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 of the chain rule is:

          So, the result is:

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

          1. Let .

          2. The derivative of sine is cosine:

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

            1. 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 of the chain rule is:

          So, the result is:

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
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$$0$$
The second derivative [src]
0
$$0$$
The third derivative [src]
0
$$0$$