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y=(1+x^(2))^ctgx

Derivada de y=(1+x^(2))^ctgx

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

Gráfico:

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Solución

Ha introducido [src]
        cot(x)
/     2\      
\1 + x /      
$$\left(x^{2} + 1\right)^{\cot{\left(x \right)}}$$
(1 + x^2)^cot(x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
        cot(x)                                          
/     2\       //        2   \    /     2\   2*x*cot(x)\
\1 + x /      *|\-1 - cot (x)/*log\1 + x / + ----------|
               |                                    2  |
               \                               1 + x   /
$$\left(x^{2} + 1\right)^{\cot{\left(x \right)}} \left(\frac{2 x \cot{\left(x \right)}}{x^{2} + 1} + \left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(x^{2} + 1 \right)}\right)$$
Segunda derivada [src]
        cot(x) /                                          2                  /       2   \      2                                            \
/     2\       |/  /       2   \    /     2\   2*x*cot(x)\    2*cot(x)   4*x*\1 + cot (x)/   4*x *cot(x)     /       2   \           /     2\|
\1 + x /      *||- \1 + cot (x)/*log\1 + x / + ----------|  + -------- - ----------------- - ----------- + 2*\1 + cot (x)/*cot(x)*log\1 + x /|
               ||                                     2  |          2               2                 2                                      |
               |\                                1 + x   /     1 + x           1 + x          /     2\                                       |
               \                                                                              \1 + x /                                       /
$$\left(x^{2} + 1\right)^{\cot{\left(x \right)}} \left(- \frac{4 x^{2} \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2} + 1} + \left(\frac{2 x \cot{\left(x \right)}}{x^{2} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)}\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)} \cot{\left(x \right)} + \frac{2 \cot{\left(x \right)}}{x^{2} + 1}\right)$$
Tercera derivada [src]
        cot(x) /                                          3     /       2   \                                                /                                                  /       2   \      2       \                  2                                                                       2 /       2   \       3               /       2   \       \
/     2\       |/  /       2   \    /     2\   2*x*cot(x)\    6*\1 + cot (x)/     /  /       2   \    /     2\   2*x*cot(x)\ |  cot(x)   /       2   \           /     2\   2*x*\1 + cot (x)/   2*x *cot(x)|     /       2   \     /     2\   12*x*cot(x)        2    /       2   \    /     2\   12*x *\1 + cot (x)/   16*x *cot(x)   12*x*\1 + cot (x)/*cot(x)|
\1 + x /      *||- \1 + cot (x)/*log\1 + x / + ----------|  - --------------- - 6*|- \1 + cot (x)/*log\1 + x / + ----------|*|- ------ - \1 + cot (x)/*cot(x)*log\1 + x / + ----------------- + -----------| - 2*\1 + cot (x)/ *log\1 + x / - ----------- - 4*cot (x)*\1 + cot (x)/*log\1 + x / + ------------------- + ------------ + -------------------------|
               ||                                     2  |              2         |                                     2  | |       2                                                 2                 2 |                                           2                                                       2                 3                    2         |
               |\                                1 + x   /         1 + x          \                                1 + x   / |  1 + x                                             1 + x          /     2\  |                                   /     2\                                                /     2\          /     2\                1 + x          |
               \                                                                                                             \                                                                   \1 + x /  /                                   \1 + x /                                                \1 + x /          \1 + x /                               /
$$\left(x^{2} + 1\right)^{\cot{\left(x \right)}} \left(\frac{16 x^{3} \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{12 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{12 x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x^{2} + 1} - \frac{12 x \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \cot{\left(x \right)}}{x^{2} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)}\right)^{3} - 6 \left(\frac{2 x \cot{\left(x \right)}}{x^{2} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)}\right) \left(\frac{2 x^{2} \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)} \cot{\left(x \right)} - \frac{\cot{\left(x \right)}}{x^{2} + 1}\right) - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{2} + 1 \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)} \cot^{2}{\left(x \right)} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2} + 1}\right)$$
Gráfico
Derivada de y=(1+x^(2))^ctgx