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y=cos³(log(x²-✓tgx))
Derivada de la función/ y=cos/ y=cos³(log(x²-✓tgx))

Derivada de y=cos³(log(x²-✓tgx))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   3/   / 2     ________\\
cos \log\x  - \/ tan(x) //
cos⁡3(log⁡(x2−tan⁡(x)))\cos^{3}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} 
cos(log(x^2 - sqrt(tan(x))))^3
Solución detallada

  1. Sustituimos u=cos⁡(log⁡(x2−tan⁡(x)))u = \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}.

  2. Según el principio, aplicamos: u3u^{3} tenemos 3u23 u^{2}

  3. Luego se aplica una cadena de reglas. Multiplicamos por ddxcos⁡(log⁡(x2−tan⁡(x)))\frac{d}{d x} \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}:

    1. Sustituimos u=log⁡(x2−tan⁡(x))u = \log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)}.

    2. La derivada del coseno es igual a menos el seno:

      dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

    3. Luego se aplica una cadena de reglas. Multiplicamos por ddxlog⁡(x2−tan⁡(x))\frac{d}{d x} \log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)}:

      1. Sustituimos u=x2−tan⁡(x)u = x^{2} - \sqrt{\tan{\left(x \right)}}.

      2. Derivado log⁡(u)\log{\left(u \right)} es 1u\frac{1}{u}.

      3. Luego se aplica una cadena de reglas. Multiplicamos por ddx(x2−tan⁡(x))\frac{d}{d x} \left(x^{2} - \sqrt{\tan{\left(x \right)}}\right):

        1. diferenciamos x2−tan⁡(x)x^{2} - \sqrt{\tan{\left(x \right)}} miembro por miembro:

          1. Según el principio, aplicamos: x2x^{2} tenemos 2x2 x

          2. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.

            1. Sustituimos u=tan⁡(x)u = \tan{\left(x \right)}.

            2. Según el principio, aplicamos: u\sqrt{u} tenemos 12u\frac{1}{2 \sqrt{u}}

            3. Luego se aplica una cadena de reglas. Multiplicamos por ddxtan⁡(x)\frac{d}{d x} \tan{\left(x \right)}:

              1. Reescribimos las funciones para diferenciar:

                tan⁡(x)=sin⁡(x)cos⁡(x)\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}

              2. Se aplica la regla de la derivada parcial:

                ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

                f(x)=sin⁡(x)f{\left(x \right)} = \sin{\left(x \right)} y g(x)=cos⁡(x)g{\left(x \right)} = \cos{\left(x \right)}.

                Para calcular ddxf(x)\frac{d}{d x} f{\left(x \right)}:

                1. La derivada del seno es igual al coseno:

                  ddxsin⁡(x)=cos⁡(x)\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}

                Para calcular ddxg(x)\frac{d}{d x} g{\left(x \right)}:

                1. La derivada del coseno es igual a menos el seno:

                  ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

                Ahora aplicamos la regla de la derivada de una divesión:

                sin⁡2(x)+cos⁡2(x)cos⁡2(x)\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}

              Como resultado de la secuencia de reglas:

              sin⁡2(x)+cos⁡2(x)2cos⁡2(x)tan⁡(x)\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}}}

            Entonces, como resultado: −sin⁡2(x)+cos⁡2(x)2cos⁡2(x)tan⁡(x)- \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}}}

          Como resultado de: 2x−sin⁡2(x)+cos⁡2(x)2cos⁡2(x)tan⁡(x)2 x - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}}}

        Como resultado de la secuencia de reglas:

        2x−sin⁡2(x)+cos⁡2(x)2cos⁡2(x)tan⁡(x)x2−tan⁡(x)\frac{2 x - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}}}}{x^{2} - \sqrt{\tan{\left(x \right)}}}

      Como resultado de la secuencia de reglas:

      −(2x−sin⁡2(x)+cos⁡2(x)2cos⁡2(x)tan⁡(x))sin⁡(log⁡(x2−tan⁡(x)))x2−tan⁡(x)- \frac{\left(2 x - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}}}\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}}

    Como resultado de la secuencia de reglas:

    −3(2x−sin⁡2(x)+cos⁡2(x)2cos⁡2(x)tan⁡(x))sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x)))x2−tan⁡(x)- \frac{3 \left(2 x - \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{2 \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}}}\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}}

  4. Simplificamos:

    −3(4xcos⁡2(x)tan⁡(x)−1)sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x)))2(x2tan⁡(x)−tan⁡(x))cos⁡2(x)- \frac{3 \left(4 x \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}} - 1\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{2 \left(x^{2} \sqrt{\tan{\left(x \right)}} - \tan{\left(x \right)}\right) \cos^{2}{\left(x \right)}}

Respuesta:

−3(4xcos⁡2(x)tan⁡(x)−1)sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x)))2(x2tan⁡(x)−tan⁡(x))cos⁡2(x)- \frac{3 \left(4 x \cos^{2}{\left(x \right)} \sqrt{\tan{\left(x \right)}} - 1\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{2 \left(x^{2} \sqrt{\tan{\left(x \right)}} - \tan{\left(x \right)}\right) \cos^{2}{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                              /             2   \                          
                              |      1   tan (x)|                          
                              |      - + -------|                          
      2/   / 2     ________\\ |      2      2   |    /   / 2     ________\\
-3*cos \log\x  - \/ tan(x) //*|2*x - -----------|*sin\log\x  - \/ tan(x) //
                              |         ________|                          
                              \       \/ tan(x) /                          
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                               2     ________                              
                              x  - \/ tan(x)
−3(2x−tan⁡2(x)2+12tan⁡(x))sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x)))x2−tan⁡(x)- \frac{3 \left(2 x - \frac{\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}}{\sqrt{\tan{\left(x \right)}}}\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}}
Simplificar
Segunda derivada [src] 
  /                     2                                                                                                                                                           2                                                 2                                                    \                          
  |  /             2   \                                                                                                                                         /             2   \                               /             2   \                                                     |                          
  |  |      1 + tan (x)|     2/   / 2     ________\\                                                                                                             |      1 + tan (x)|     2/   / 2     ________\\   |      1 + tan (x)|     /   / 2     ________\\    /   / 2     ________\\|                          
  |  |4*x - -----------| *cos \log\x  - \/ tan(x) //   /                 2                             \                                                       2*|4*x - -----------| *sin \log\x  - \/ tan(x) //   |4*x - -----------| *cos\log\x  - \/ tan(x) //*sin\log\x  - \/ tan(x) //|                          
  |  |         ________|                               |    /       2   \                              |                                                         |         ________|                               |         ________|                                                     |                          
  |  \       \/ tan(x) /                               |    \1 + tan (x)/        ________ /       2   \|    /   / 2     ________\\    /   / 2     ________\\     \       \/ tan(x) /                               \       \/ tan(x) /                                                     |    /   / 2     ________\\
3*|- ----------------------------------------------- - |8 + -------------- - 4*\/ tan(x) *\1 + tan (x)/|*cos\log\x  - \/ tan(x) //*sin\log\x  - \/ tan(x) // + ------------------------------------------------- + ------------------------------------------------------------------------|*cos\log\x  - \/ tan(x) //
  |                   2     ________                   |         3/2                                   |                                                                         2     ________                                                 2     ________                             |                          
  \                  x  - \/ tan(x)                    \      tan   (x)                                /                                                                        x  - \/ tan(x)                                                 x  - \/ tan(x)                              /                          
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                                                                                                                                                   / 2     ________\                                                                                                                                                  
                                                                                                                                                 4*\x  - \/ tan(x) /
3(2(4x−tan⁡2(x)+1tan⁡(x))2sin⁡2(log⁡(x2−tan⁡(x)))x2−tan⁡(x)+(4x−tan⁡2(x)+1tan⁡(x))2sin⁡(log⁡(x2−tan⁡(x)))cos⁡(log⁡(x2−tan⁡(x)))x2−tan⁡(x)−(4x−tan⁡2(x)+1tan⁡(x))2cos⁡2(log⁡(x2−tan⁡(x)))x2−tan⁡(x)−((tan⁡2(x)+1)2tan⁡32(x)−4(tan⁡2(x)+1)tan⁡(x)+8)sin⁡(log⁡(x2−tan⁡(x)))cos⁡(log⁡(x2−tan⁡(x))))cos⁡(log⁡(x2−tan⁡(x)))4(x2−tan⁡(x))\frac{3 \left(\frac{2 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{2} \sin^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}} + \frac{\left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{2} \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}} - \frac{\left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{2} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}} - \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}} + 8\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}\right) \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{4 \left(x^{2} - \sqrt{\tan{\left(x \right)}}\right)}
Simplificar
Tercera derivada [src] 
  /                       3                                                   3                                                                                                                                                                            3                                                                                                         /                 2                             \                        3                                                                                                         /                 2                             \                                                                              /                 2                             \                          \
  |    /             2   \                                 /             2   \                                                                                                                                                          /             2   \                                                                                      /             2   \ |    /       2   \                              |     /             2   \                                                                                      /             2   \ |    /       2   \                              |                                                          /             2   \ |    /       2   \                              |                          |
  |    |      1 + tan (x)|     3/   / 2     ________\\     |      1 + tan (x)|     3/   / 2     ________\\                                                                                                                              |      1 + tan (x)|     2/   / 2     ________\\    /   / 2     ________\\        3/   / 2     ________\\ |      1 + tan (x)| |    \1 + tan (x)/        ________ /       2   \|     |      1 + tan (x)|     2/   / 2     ________\\    /   / 2     ________\\        2/   / 2     ________\\ |      1 + tan (x)| |    \1 + tan (x)/        ________ /       2   \|    /   / 2     ________\\        2/   / 2     ________\\ |      1 + tan (x)| |    \1 + tan (x)/        ________ /       2   \|    /   / 2     ________\\|
  |  2*|4*x - -----------| *sin \log\x  - \/ tan(x) //   3*|4*x - -----------| *cos \log\x  - \/ tan(x) //                                            /                                                2\                             6*|4*x - -----------| *sin \log\x  - \/ tan(x) //*cos\log\x  - \/ tan(x) //   3*cos \log\x  - \/ tan(x) //*|4*x - -----------|*|8 + -------------- - 4*\/ tan(x) *\1 + tan (x)/|   5*|4*x - -----------| *cos \log\x  - \/ tan(x) //*sin\log\x  - \/ tan(x) //   3*cos \log\x  - \/ tan(x) //*|4*x - -----------|*|8 + -------------- - 4*\/ tan(x) *\1 + tan (x)/|*sin\log\x  - \/ tan(x) //   6*sin \log\x  - \/ tan(x) //*|4*x - -----------|*|8 + -------------- - 4*\/ tan(x) *\1 + tan (x)/|*cos\log\x  - \/ tan(x) //|
  |    |         ________|                                 |         ________|                                                                        |                 /       2   \     /       2   \ |                               |         ________|                                                                                      |         ________| |         3/2                                   |     |         ________|                                                                                      |         ________| |         3/2                                   |                                                          |         ________| |         3/2                                   |                          |
  |    \       \/ tan(x) /                                 \       \/ tan(x) /                                  2/   / 2     ________\\ /       2   \ |      3/2      4*\1 + tan (x)/   3*\1 + tan (x)/ |    /   / 2     ________\\     \       \/ tan(x) /                                                                                      \       \/ tan(x) / \      tan   (x)                                /     \       \/ tan(x) /                                                                                      \       \/ tan(x) / \      tan   (x)                                /                                                          \       \/ tan(x) / \      tan   (x)                                /                          |
3*|- ------------------------------------------------- + ------------------------------------------------- + cos \log\x  - \/ tan(x) //*\1 + tan (x)/*|16*tan   (x) - --------------- + ----------------|*sin\log\x  - \/ tan(x) // - --------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------|
  |                                   2                                                   2                                                           |                    ________           5/2       |                                                                           2                                                                         2     ________                                                                                           2                                                                                      2     ________                                                                                                                 2     ________                                                       |
  |                  / 2     ________\                                   / 2     ________\                                                            \                  \/ tan(x)         tan   (x)    /                                                          / 2     ________\                                                                         x  - \/ tan(x)                                                                           / 2     ________\                                                                                      x  - \/ tan(x)                                                                                                                 x  - \/ tan(x)                                                        |
  \                  \x  - \/ tan(x) /                                   \x  - \/ tan(x) /                                                                                                                                                                         \x  - \/ tan(x) /                                                                                                                                                                  \x  - \/ tan(x) /                                                                                                                                                                                                                                                                                           /
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                                                                                                                                                                                                                                                                                                                                                                          / 2     ________\                                                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                                                                                                                                        8*\x  - \/ tan(x) /
3(−2(4x−tan⁡2(x)+1tan⁡(x))3sin⁡3(log⁡(x2−tan⁡(x)))(x2−tan⁡(x))2−6(4x−tan⁡2(x)+1tan⁡(x))3sin⁡2(log⁡(x2−tan⁡(x)))cos⁡(log⁡(x2−tan⁡(x)))(x2−tan⁡(x))2+5(4x−tan⁡2(x)+1tan⁡(x))3sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x)))(x2−tan⁡(x))2+3(4x−tan⁡2(x)+1tan⁡(x))3cos⁡3(log⁡(x2−tan⁡(x)))(x2−tan⁡(x))2+6(4x−tan⁡2(x)+1tan⁡(x))((tan⁡2(x)+1)2tan⁡32(x)−4(tan⁡2(x)+1)tan⁡(x)+8)sin⁡2(log⁡(x2−tan⁡(x)))cos⁡(log⁡(x2−tan⁡(x)))x2−tan⁡(x)+3(4x−tan⁡2(x)+1tan⁡(x))((tan⁡2(x)+1)2tan⁡32(x)−4(tan⁡2(x)+1)tan⁡(x)+8)sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x)))x2−tan⁡(x)−3(4x−tan⁡2(x)+1tan⁡(x))((tan⁡2(x)+1)2tan⁡32(x)−4(tan⁡2(x)+1)tan⁡(x)+8)cos⁡3(log⁡(x2−tan⁡(x)))x2−tan⁡(x)+(tan⁡2(x)+1)(3(tan⁡2(x)+1)2tan⁡52(x)−4(tan⁡2(x)+1)tan⁡(x)+16tan⁡32(x))sin⁡(log⁡(x2−tan⁡(x)))cos⁡2(log⁡(x2−tan⁡(x))))8(x2−tan⁡(x))\frac{3 \left(- \frac{2 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{3} \sin^{3}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{\left(x^{2} - \sqrt{\tan{\left(x \right)}}\right)^{2}} - \frac{6 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{3} \sin^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{\left(x^{2} - \sqrt{\tan{\left(x \right)}}\right)^{2}} + \frac{5 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{3} \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{\left(x^{2} - \sqrt{\tan{\left(x \right)}}\right)^{2}} + \frac{3 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right)^{3} \cos^{3}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{\left(x^{2} - \sqrt{\tan{\left(x \right)}}\right)^{2}} + \frac{6 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}} + 8\right) \sin^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}} + \frac{3 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}} + 8\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}} - \frac{3 \left(4 x - \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}} + 8\right) \cos^{3}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}}{x^{2} - \sqrt{\tan{\left(x \right)}}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x \right)}\right) \sin{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)} \cos^{2}{\left(\log{\left(x^{2} - \sqrt{\tan{\left(x \right)}} \right)} \right)}\right)}{8 \left(x^{2} - \sqrt{\tan{\left(x \right)}}\right)}
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Gráfico
Derivada de y=cos³(log(x²-✓tgx))
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