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 6/x
-
Derivada de 2*sqrt(x)
-
Derivada de e^(5*x)
-
Derivada de 1+x
-
Expresiones idénticas
- y=(arctan(2x))^x
- y es igual a (arc tangente de (2x)) en el grado x
- y=(arctan(2x))x
- y=arctan2xx
- y=arctan2x^x
-
Expresiones con funciones
- arctan
- arctanx
- arctanh(sin2x)
- arctan((x-1)/2)
- arctan(x^3)
Derivada de y=(arctan(2x))^x
Solución
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
x / 2*x \
atan (2*x)*|-------------------- + log(atan(2*x))|
|/ 2\ |
\\1 + 4*x /*atan(2*x) /
$$\left(\frac{2 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}\right) \operatorname{atan}^{x}{\left(2 x \right)}$$
Segunda derivada
[src]
/ / 2 \\
| | 4*x x ||
| 4*|-1 + -------- + --------------------||
| 2 | 2 / 2\ ||
x |/ 2*x \ \ 1 + 4*x \1 + 4*x /*atan(2*x)/|
atan (2*x)*||-------------------- + log(atan(2*x))| - ----------------------------------------|
||/ 2\ | / 2\ |
\\\1 + 4*x /*atan(2*x) / \1 + 4*x /*atan(2*x) /
$$\left(\left(\frac{2 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}\right)^{2} - \frac{4 \left(\frac{4 x^{2}}{4 x^{2} + 1} + \frac{x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 1\right)}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}\right) \operatorname{atan}^{x}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 3 2 \ / 2 \\
| | 3 64*x 4*x 24*x | / 2*x \ | 4*x x ||
| 4*|-16*x - --------- + -------- + --------------------- + --------------------| 12*|-------------------- + log(atan(2*x))|*|-1 + -------- + --------------------||
| 3 | atan(2*x) 2 / 2\ 2 / 2\ | |/ 2\ | | 2 / 2\ ||
x |/ 2*x \ \ 1 + 4*x \1 + 4*x /*atan (2*x) \1 + 4*x /*atan(2*x)/ \\1 + 4*x /*atan(2*x) / \ 1 + 4*x \1 + 4*x /*atan(2*x)/|
atan (2*x)*||-------------------- + log(atan(2*x))| + ------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------|
||/ 2\ | 2 / 2\ |
|\\1 + 4*x /*atan(2*x) / / 2\ \1 + 4*x /*atan(2*x) |
\ \1 + 4*x / *atan(2*x) /
$$\left(\left(\frac{2 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}\right)^{3} - \frac{12 \left(\frac{2 x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}\right) \left(\frac{4 x^{2}}{4 x^{2} + 1} + \frac{x}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 1\right)}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{4 \left(\frac{64 x^{3}}{4 x^{2} + 1} + \frac{24 x^{2}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - 16 x + \frac{4 x}{\left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}} - \frac{3}{\operatorname{atan}{\left(2 x \right)}}\right)}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}}\right) \operatorname{atan}^{x}{\left(2 x \right)}$$
Gráfico