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 (x+1)^2
-
Derivada de x^(2/3)
-
Derivada de e^(2*x)
-
Derivada de 3^x
-
Expresiones idénticas
- x^e^cot(x)
- x en el grado e en el grado cotangente de (x)
- xecot(x)
- xecotx
- x^e^cotx
-
Expresiones con funciones
- Cotangente cot
- cot(x)^3
- cot(x)^(4)
- cot(x)/((6*x))
- cot(1/x)
- cot(x)/x
Derivada de x^e^cot(x)
Solución
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
Simplificamos:
Respuesta:
Primera derivada
[src]
/ cot(x)\ / cot(x) \
\E / |e / 2 \ cot(x) |
x *|------- + \-1 - cot (x)/*e *log(x)|
\ x /
$$x^{e^{\cot{\left(x \right)}}} \left(\left(- \cot^{2}{\left(x \right)} - 1\right) e^{\cot{\left(x \right)}} \log{\left(x \right)} + \frac{e^{\cot{\left(x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ cot(x)\ / 2 2 / 2 \ \
\e / | 1 / 2 \ / 1 / 2 \ \ cot(x) 2*\1 + cot (x)/ / 2 \ | cot(x)
x *|- -- + \1 + cot (x)/ *log(x) + |- - + \1 + cot (x)/*log(x)| *e - --------------- + 2*\1 + cot (x)/*cot(x)*log(x)|*e
| 2 \ x / x |
\ x /
$$x^{e^{\cot{\left(x \right)}}} \left(\left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{1}{x}\right)^{2} e^{\cot{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{\cot{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 \
/ cot(x)\ | 3 3 / 2 \ / 2 \ 2 / 2 \ / 2 / 2 \ \ 2 |
\e / | 2 / 2 \ / 1 / 2 \ \ 2*cot(x) 3*\1 + cot (x)/ 3*\1 + cot (x)/ / 2 \ 6*\1 + cot (x)/*cot(x) / 1 / 2 \ \ | 1 / 2 \ 2*\1 + cot (x)/ / 2 \ | cot(x) 2 / 2 \ / 2 \ | cot(x)
-x *|- -- + \1 + cot (x)/ *log(x) + |- - + \1 + cot (x)/*log(x)| *e - ---------------- - --------------- + 2*\1 + cot (x)/ *log(x) - ---------------------- + 3*|- - + \1 + cot (x)/*log(x)|*|- -- + \1 + cot (x)/ *log(x) - --------------- + 2*\1 + cot (x)/*cot(x)*log(x)|*e + 4*cot (x)*\1 + cot (x)/*log(x) + 6*\1 + cot (x)/ *cot(x)*log(x)|*e
| 3 \ x / x 2 x \ x / | 2 x | |
\ x x \ x / /
$$- x^{e^{\cot{\left(x \right)}}} \left(\left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{1}{x}\right)^{3} e^{2 \cot{\left(x \right)}} + 3 \left(\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{1}{x}\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot{\left(x \right)} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right) e^{\cot{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \log{\left(x \right)} + 6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} \cot{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot^{2}{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{x} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2}{x^{3}}\right) e^{\cot{\left(x \right)}}$$