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Derivada de:
Derivada de 3/x
Derivada de -e^-x
Derivada de x+4
Derivada de x*atan(x)
Expresiones idénticas
y=(ctg3x)^x^ dos
y es igual a (ctg3x) en el grado x al cuadrado
y es igual a (ctg3x) en el grado x en el grado dos
y=(ctg3x)x2
y=ctg3xx2
y=(ctg3x)^x²
y=(ctg3x) en el grado x en el grado 2
y=ctg3x^x^2

Derivada de la función/ ctg3x/ y=(ctg3x)^x^2

Derivada de y=(ctg3x)^x^2

Solución

Ha introducido [src]

          / 2\
          \x /
(cot(3*x))

$$\cot^{x^{2}}{\left(3 x \right)}$$

cot(3*x)^(x^2)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

          / 2\ /                     2 /          2     \\
          \x / |                    x *\-3 - 3*cot (3*x)/|
(cot(3*x))    *|2*x*log(cot(3*x)) + ---------------------|
               \                           cot(3*x)      /

$$\left(\frac{x^{2} \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right)}{\cot{\left(3 x \right)}} + 2 x \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{x^{2}}{\left(3 x \right)}$$

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Segunda derivada [src]

               /                                                             2                                                                      2\
          / 2\ |                     /                       /       2     \\                                 /       2     \      2 /       2     \ |
          \x / |                   2 |                   3*x*\1 + cot (3*x)/|        2 /       2     \   12*x*\1 + cot (3*x)/   9*x *\1 + cot (3*x)/ |
(cot(3*x))    *|2*log(cot(3*x)) + x *|-2*log(cot(3*x)) + -------------------|  + 18*x *\1 + cot (3*x)/ - -------------------- - ---------------------|
               |                     \                         cot(3*x)     /                                  cot(3*x)                  2           |
               \                                                                                                                      cot (3*x)      /

$$\left(x^{2} \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right)^{2} - \frac{9 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + 18 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right) - \frac{12 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{x^{2}}{\left(3 x \right)}$$

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Tercera derivada [src]

               /                                             3                      /                                                                                                  2\                                                /                                                               2                       \\
          / 2\ |     /                       /       2     \\                       |                                    2 /       2     \       /       2     \      2 /       2     \ |       /                       /       2     \\ |                                              2 /       2     \         /       2     \||
          \x / |   3 |                   3*x*\1 + cot (3*x)/|       /       2     \ |   1                2            6*x *\1 + cot (3*x)/   3*x*\1 + cot (3*x)/   3*x *\1 + cot (3*x)/ |       |                   3*x*\1 + cot (3*x)/| |                       2 /       2     \   9*x *\1 + cot (3*x)/    12*x*\1 + cot (3*x)/||
(cot(3*x))    *|- x *|-2*log(cot(3*x)) + -------------------|  - 18*\1 + cot (3*x)/*|-------- - 6*x + 6*x *cot(3*x) - -------------------- + ------------------- + ---------------------| + 3*x*|-2*log(cot(3*x)) + -------------------|*|-2*log(cot(3*x)) - 18*x *\1 + cot (3*x)/ + --------------------- + --------------------||
               |     \                         cot(3*x)     /                       |cot(3*x)                               cot(3*x)                 2                      3           |       \                         cot(3*x)     / |                                                    2                    cot(3*x)      ||
               \                                                                    \                                                             cot (3*x)              cot (3*x)      /                                                \                                                 cot (3*x)                             //

$$\left(- x^{3} \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right)^{3} + 3 x \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) \left(\frac{9 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - 18 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right) + \frac{12 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(\frac{3 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{3}{\left(3 x \right)}} - \frac{6 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 6 x^{2} \cot{\left(3 x \right)} + \frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot^{2}{\left(3 x \right)}} - 6 x + \frac{1}{\cot{\left(3 x \right)}}\right)\right) \cot^{x^{2}}{\left(3 x \right)}$$

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Gráfico

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Expresiones idénticas

Derivada de y=(ctg3x)^x^2

Gráfico:

Definida a trozos:

Solución