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Derivative of sen(2x)ln((x-1)^(1/2))

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

The graph:

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Piecewise:

The solution

You have entered [src]
            /  _______\
sin(2*x)*log\\/ x - 1 /
$$\log{\left(\sqrt{x - 1} \right)} \sin{\left(2 x \right)}$$
sin(2*x)*log(sqrt(x - 1))
Detail solution
  1. Apply the product rule:

    ; to find :

    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:

    ; to find :

    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. Apply the power rule: goes to

          2. The derivative of the constant is zero.

          The result is:

        The result of the chain rule is:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 sin(2*x)                 /  _______\
--------- + 2*cos(2*x)*log\\/ x - 1 /
2*(x - 1)                            
$$2 \log{\left(\sqrt{x - 1} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{2 \left(x - 1\right)}$$
The second derivative [src]
       /  ________\            2*cos(2*x)     sin(2*x) 
- 4*log\\/ -1 + x /*sin(2*x) + ---------- - -----------
                                 -1 + x               2
                                            2*(-1 + x) 
$$- 4 \log{\left(\sqrt{x - 1} \right)} \sin{\left(2 x \right)} + \frac{2 \cos{\left(2 x \right)}}{x - 1} - \frac{\sin{\left(2 x \right)}}{2 \left(x - 1\right)^{2}}$$
The third derivative [src]
 sin(2*x)                 /  ________\   6*sin(2*x)   3*cos(2*x)
--------- - 8*cos(2*x)*log\\/ -1 + x / - ---------- - ----------
        3                                  -1 + x             2 
(-1 + x)                                              (-1 + x)  
$$- 8 \log{\left(\sqrt{x - 1} \right)} \cos{\left(2 x \right)} - \frac{6 \sin{\left(2 x \right)}}{x - 1} - \frac{3 \cos{\left(2 x \right)}}{\left(x - 1\right)^{2}} + \frac{\sin{\left(2 x \right)}}{\left(x - 1\right)^{3}}$$