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Derivada de la función/ sin^2/ ln^2x/ y=(sin^2x)^ln^2x

Derivada de y=(sin^2x)^ln^2x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
          2   
       log (x)
   2          
sin (x)
(sin⁡2(x))log⁡(x)2\left(\sin^{2}{\left(x \right)}\right)^{\log{\left(x \right)}^{2}} 
(sin(x)^2)^(log(x)^2)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(log⁡(x)2)+1)(log⁡(x)2)log⁡(x)2\left(\log{\left(\log{\left(x \right)}^{2} \right)} + 1\right) \left(\log{\left(x \right)}^{2}\right)^{\log{\left(x \right)}^{2}}

Respuesta:

(log⁡(log⁡(x)2)+1)(log⁡(x)2)log⁡(x)2\left(\log{\left(\log{\left(x \right)}^{2} \right)} + 1\right) \left(\log{\left(x \right)}^{2}\right)^{\log{\left(x \right)}^{2}}

Primera derivada [src] 
             2    /            /   2   \        2          \
        2*log (x) |2*log(x)*log\sin (x)/   2*log (x)*cos(x)|
|sin(x)|         *|--------------------- + ----------------|
                  \          x                  sin(x)     /
(2log⁡(x)2cos⁡(x)sin⁡(x)+2log⁡(x)log⁡(sin⁡2(x))x)∣sin⁡(x)∣2log⁡(x)2\left(\frac{2 \log{\left(x \right)}^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left|{\sin{\left(x \right)}}\right|^{2 \log{\left(x \right)}^{2}}
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Segunda derivada [src] 
               2    /               /   2   \             /   2   \      2       2                /   /   2   \                \                                                                 \
          2*log (x) |     2      log\sin (x)/   log(x)*log\sin (x)/   cos (x)*log (x)        2    |log\sin (x)/   cos(x)*log(x)| /2*log(|sin(x)|)   cos(x)*log(x)*sign(sin(x))\   4*cos(x)*log(x)|
2*|sin(x)|         *|- log (x) + ------------ - ------------------- - --------------- + 2*log (x)*|------------ + -------------|*|--------------- + --------------------------| + ---------------|
                    |                  2                  2                  2                    \     x             sin(x)   / \       x                   |sin(x)|         /       x*sin(x)   |
                    \                 x                  x                sin (x)                                                                                                                /
2(2(log⁡(x)cos⁡(x)sin⁡(x)+log⁡(sin⁡2(x))x)(log⁡(x)cos⁡(x)sign⁡(sin⁡(x))∣sin⁡(x)∣+2log⁡(∣sin⁡(x)∣)x)log⁡(x)2−log⁡(x)2−log⁡(x)2cos⁡2(x)sin⁡2(x)+4log⁡(x)cos⁡(x)xsin⁡(x)−log⁡(x)log⁡(sin⁡2(x))x2+log⁡(sin⁡2(x))x2)∣sin⁡(x)∣2log⁡(x)22 \left(2 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x}\right) \log{\left(x \right)}^{2} - \log{\left(x \right)}^{2} - \frac{\log{\left(x \right)}^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4 \log{\left(x \right)} \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{\log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}}\right) \left|{\sin{\left(x \right)}}\right|^{2 \log{\left(x \right)}^{2}}
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Tercera derivada [src] 
               2    /                  /   2   \                                                    /             /   2   \             /   2   \      2       2                     \            /   /   2   \                \ /                                                2                             2       2        2                2       2                                                     \                      /   2   \        3       2           2                                                             2         /   /   2   \                \                    2                            \
          2*log (x) |  6*log(x)   3*log\sin (x)/     /2*log(|sin(x)|)   cos(x)*log(x)*sign(sin(x))\ |   2      log\sin (x)/   log(x)*log\sin (x)/   cos (x)*log (x)   4*cos(x)*log(x)|            |log\sin (x)/   cos(x)*log(x)| |  2*log(|sin(x)|)   2*log(x)*log(|sin(x)|)   log (x)*sign(sin(x))*sin(x)   cos (x)*log (x)*sign (sin(x))   2*cos (x)*log (x)*DiracDelta(sin(x))   4*cos(x)*log(x)*sign(sin(x))|          2*log(x)*log\sin (x)/   2*cos (x)*log (x)   2*log (x)*cos(x)     /2*log(|sin(x)|)   cos(x)*log(x)*sign(sin(x))\     3    |log\sin (x)/   cos(x)*log(x)|    6*cos(x)   6*cos (x)*log(x)   6*cos(x)*log(x)|
2*|sin(x)|         *|- -------- - -------------- - 4*|--------------- + --------------------------|*|log (x) - ------------ + ------------------- + --------------- - ---------------|*log(x) - 2*|------------ + -------------|*|- --------------- + ---------------------- + --------------------------- + ----------------------------- - ------------------------------------ - ----------------------------|*log(x) + --------------------- + ----------------- + ---------------- + 4*|--------------- + --------------------------| *log (x)*|------------ + -------------| + --------- - ---------------- - ---------------|
                    |     x              3           \       x                   |sin(x)|         / |                2                  2                  2              x*sin(x)   |            \     x             sin(x)   / |          2                    2                       |sin(x)|                          2                               |sin(x)|                          x*|sin(x)|         |                     3                    3                sin(x)          \       x                   |sin(x)|         /          \     x             sin(x)   /    2                  2              2          |
                    \                   x                                                           \               x                  x                sin (x)                      /                                           \         x                    x                                                       sin (x)                                                                                 /                    x                  sin (x)                                                                                                                      x *sin(x)      x*sin (x)          x *sin(x)   /
2(4(log⁡(x)cos⁡(x)sin⁡(x)+log⁡(sin⁡2(x))x)(log⁡(x)cos⁡(x)sign⁡(sin⁡(x))∣sin⁡(x)∣+2log⁡(∣sin⁡(x)∣)x)2log⁡(x)3−2(log⁡(x)cos⁡(x)sin⁡(x)+log⁡(sin⁡2(x))x)(log⁡(x)2sin⁡(x)sign⁡(sin⁡(x))∣sin⁡(x)∣−2log⁡(x)2cos⁡2(x)δ(sin⁡(x))∣sin⁡(x)∣+log⁡(x)2cos⁡2(x)sign⁡2(sin⁡(x))sin⁡2(x)−4log⁡(x)cos⁡(x)sign⁡(sin⁡(x))x∣sin⁡(x)∣+2log⁡(x)log⁡(∣sin⁡(x)∣)x2−2log⁡(∣sin⁡(x)∣)x2)log⁡(x)−4(log⁡(x)cos⁡(x)sign⁡(sin⁡(x))∣sin⁡(x)∣+2log⁡(∣sin⁡(x)∣)x)(log⁡(x)2+log⁡(x)2cos⁡2(x)sin⁡2(x)−4log⁡(x)cos⁡(x)xsin⁡(x)+log⁡(x)log⁡(sin⁡2(x))x2−log⁡(sin⁡2(x))x2)log⁡(x)+2log⁡(x)2cos⁡(x)sin⁡(x)+2log⁡(x)2cos⁡3(x)sin⁡3(x)−6log⁡(x)x−6log⁡(x)cos⁡2(x)xsin⁡2(x)−6log⁡(x)cos⁡(x)x2sin⁡(x)+6cos⁡(x)x2sin⁡(x)+2log⁡(x)log⁡(sin⁡2(x))x3−3log⁡(sin⁡2(x))x3)∣sin⁡(x)∣2log⁡(x)22 \left(4 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x}\right)^{2} \log{\left(x \right)}^{3} - 2 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)}^{2} \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} - \frac{2 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right)}{\left|{\sin{\left(x \right)}}\right|} + \frac{\log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{x \left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(x \right)} \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x^{2}} - \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x^{2}}\right) \log{\left(x \right)} - 4 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x}\right) \left(\log{\left(x \right)}^{2} + \frac{\log{\left(x \right)}^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \log{\left(x \right)} \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}} - \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{2 \log{\left(x \right)}^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{6 \log{\left(x \right)}}{x} - \frac{6 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{6 \log{\left(x \right)} \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{6 \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{3}} - \frac{3 \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{3}}\right) \left|{\sin{\left(x \right)}}\right|^{2 \log{\left(x \right)}^{2}}
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