Sr Examen

Derivada de y=(lnx)^ctg7x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
   cot(7*x)   
log        (x)
$$\log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
log(x)^cot(7*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Primera derivada [src]
   cot(7*x)    //          2     \               cot(7*x)\
log        (x)*|\-7 - 7*cot (7*x)/*log(log(x)) + --------|
               \                                 x*log(x)/
$$\left(\left(- 7 \cot^{2}{\left(7 x \right)} - 7\right) \log{\left(\log{\left(x \right)} \right)} + \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
Segunda derivada [src]
               /                                          2                               /       2     \                                          \
   cot(7*x)    |/  /       2     \               cot(7*x)\     cot(7*x)    cot(7*x)    14*\1 + cot (7*x)/      /       2     \                     |
log        (x)*||7*\1 + cot (7*x)/*log(log(x)) - --------|  - --------- - ---------- - ------------------ + 98*\1 + cot (7*x)/*cot(7*x)*log(log(x))|
               |\                                x*log(x)/     2           2    2           x*log(x)                                               |
               \                                              x *log(x)   x *log (x)                                                               /
$$\left(\left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} - \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right)^{2} + 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \cot{\left(7 x \right)} - \frac{14 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x \log{\left(x \right)}} - \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
Tercera derivada [src]
               /                                            3                      2                                                            /                                                                      /       2     \\                                                                                          /       2     \      /       2     \       /       2     \         \
   cot(7*x)    |  /  /       2     \               cot(7*x)\        /       2     \                  /  /       2     \               cot(7*x)\ | cot(7*x)    cot(7*x)       /       2     \                        14*\1 + cot (7*x)/|           2      /       2     \               2*cot(7*x)   2*cot(7*x)   3*cot(7*x)   21*\1 + cot (7*x)/   21*\1 + cot (7*x)/   294*\1 + cot (7*x)/*cot(7*x)|
log        (x)*|- |7*\1 + cot (7*x)/*log(log(x)) - --------|  - 686*\1 + cot (7*x)/ *log(log(x)) + 3*|7*\1 + cot (7*x)/*log(log(x)) - --------|*|--------- + ---------- - 98*\1 + cot (7*x)/*cot(7*x)*log(log(x)) + ------------------| - 1372*cot (7*x)*\1 + cot (7*x)/*log(log(x)) + ---------- + ---------- + ---------- + ------------------ + ------------------ + ----------------------------|
               |  \                                x*log(x)/                                         \                                x*log(x)/ | 2           2    2                                                     x*log(x)     |                                                 3            3    3       3    2           2                    2    2                    x*log(x)          |
               \                                                                                                                                \x *log(x)   x *log (x)                                                               /                                                x *log(x)    x *log (x)   x *log (x)       x *log(x)            x *log (x)                                   /
$$\left(- \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} - \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right)^{3} + 3 \left(7 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} - \frac{\cot{\left(7 x \right)}}{x \log{\left(x \right)}}\right) \left(- 98 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \cot{\left(7 x \right)} + \frac{14 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x \log{\left(x \right)}} + \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\cot{\left(7 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - 686 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} \log{\left(\log{\left(x \right)} \right)} - 1372 \left(\cot^{2}{\left(7 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \cot^{2}{\left(7 x \right)} + \frac{294 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)}}{x \log{\left(x \right)}} + \frac{21 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x^{2} \log{\left(x \right)}} + \frac{21 \left(\cot^{2}{\left(7 x \right)} + 1\right)}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \cot{\left(7 x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \cot{\left(7 x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \cot{\left(7 x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\cot{\left(7 x \right)}}$$
Gráfico
Derivada de y=(lnx)^ctg7x