Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
-
¿Cómo usar?
- Derivada de:
-
Derivada de 1/(x+3)
-
Derivada de x^(5*x)
-
Derivada de x^3/6
-
Derivada de x^-8
-
Expresiones idénticas
- x^exp(x)^ctg(x)
- x en el grado exponente de (x) en el grado ctg(x)
- xexp(x)ctg(x)
- xexpxctgx
- x^expx^ctgx
Derivada de x^exp(x)^ctg(x)
Solución
Ha introducido
[src]
/ cot(x)\ |/ x\ | \\e / / x
$$x^{\left(e^{x}\right)^{\cot{\left(x \right)}}}$$
x^(exp(x)^cot(x))
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
Simplificamos:
Respuesta:
Primera derivada
[src]
/ cot(x)\
|/ x\ | / x*cot(x) \
\\e / / |e / / 2 \ \ x*cot(x) |
x *|--------- + \x*\-1 - cot (x)/ + cot(x)/*e *log(x)|
\ x /
$$x^{\left(e^{x}\right)^{\cot{\left(x \right)}}} \left(\left(x \left(- \cot^{2}{\left(x \right)} - 1\right) + \cot{\left(x \right)}\right) e^{x \cot{\left(x \right)}} \log{\left(x \right)} + \frac{e^{x \cot{\left(x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ x*cot(x)\ / 2 2 / / 2 \\ \
\e / | 1 / 1 / / 2 \\ \ x*cot(x) / / 2 \\ 2*\-cot(x) + x*\1 + cot (x)// / 2 / 2 \ \ | x*cot(x)
x *|- -- + |- - + \-cot(x) + x*\1 + cot (x)//*log(x)| *e + \-cot(x) + x*\1 + cot (x)// *log(x) - ----------------------------- - 2*\1 + cot (x) - x*\1 + cot (x)/*cot(x)/*log(x)|*e
| 2 \ x / x |
\ x /
$$x^{e^{x \cot{\left(x \right)}}} \left(\left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)^{2} \log{\left(x \right)} + \left(\left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{2} e^{x \cot{\left(x \right)}} - 2 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{2 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)}{x} - \frac{1}{x^{2}}\right) e^{x \cot{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 \
/ x*cot(x)\ | 3 3 / 2 / 2 \ \ / / 2 \\ / / 2 \\ / 2 / / 2 \\ \ |
\e / |2 / 1 / / 2 \\ \ 2*x*cot(x) / / 2 \\ 6*\1 + cot (x) - x*\1 + cot (x)/*cot(x)/ 3*\-cot(x) + x*\1 + cot (x)// 3*\-cot(x) + x*\1 + cot (x)// / 2 \ / / 2 \ 2 \ / 1 / / 2 \\ \ |1 / / 2 \\ 2*\-cot(x) + x*\1 + cot (x)// / 2 / 2 \ \ | x*cot(x) / / 2 \\ / 2 / 2 \ \ | x*cot(x)
x *|-- - |- - + \-cot(x) + x*\1 + cot (x)//*log(x)| *e - \-cot(x) + x*\1 + cot (x)// *log(x) - ---------------------------------------- + ------------------------------ + ----------------------------- - 2*\1 + cot (x)/*\-3*cot(x) + x*\1 + cot (x)/ + 2*x*cot (x)/*log(x) + 3*|- - + \-cot(x) + x*\1 + cot (x)//*log(x)|*|-- - \-cot(x) + x*\1 + cot (x)// *log(x) + ----------------------------- + 2*\1 + cot (x) - x*\1 + cot (x)/*cot(x)/*log(x)|*e + 6*\-cot(x) + x*\1 + cot (x)//*\1 + cot (x) - x*\1 + cot (x)/*cot(x)/*log(x)|*e
| 3 \ x / x x 2 \ x / | 2 x | |
\x x \x / /
$$x^{e^{x \cot{\left(x \right)}}} \left(- \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)^{3} \log{\left(x \right)} + 6 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right) \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \left(\left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right) \log{\left(x \right)} - \frac{1}{x}\right)^{3} e^{2 x \cot{\left(x \right)}} + 3 \left(\left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right) \log{\left(x \right)} - \frac{1}{x}\right) \left(- \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)^{2} \log{\left(x \right)} + 2 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{2 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)}{x} + \frac{1}{x^{2}}\right) e^{x \cot{\left(x \right)}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(x \left(\cot^{2}{\left(x \right)} + 1\right) + 2 x \cot^{2}{\left(x \right)} - 3 \cot{\left(x \right)}\right) \log{\left(x \right)} + \frac{3 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)^{2}}{x} - \frac{6 \left(- x \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right)}{x} + \frac{3 \left(x \left(\cot^{2}{\left(x \right)} + 1\right) - \cot{\left(x \right)}\right)}{x^{2}} + \frac{2}{x^{3}}\right) e^{x \cot{\left(x \right)}}$$