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
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¿Cómo usar?
- Derivada de:
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Derivada de 1/(x+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=(arctg2x)^(uno /x)
- y es igual a (arctg2x) en el grado (1 dividir por x)
- y es igual a (arctg2x) en el grado (uno dividir por x)
- y=(arctg2x)(1/x)
- y=arctg2x1/x
- y=arctg2x^1/x
- y=(arctg2x)^(1 dividir por x)
Derivada de y=(arctg2x)^(1/x)
Solución
Ha introducido
[src]
x ___________ \/ atan(2*x)
$$\operatorname{atan}^{\frac{1}{x}}{\left(2 x \right)}$$
atan(2*x)^(1/x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
x ___________ / log(atan(2*x)) 2 \
\/ atan(2*x) *|- -------------- + ----------------------|
| 2 / 2\ |
\ x x*\1 + 4*x /*atan(2*x)/
$$\left(\frac{2}{x \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\frac{1}{x}}{\left(2 x \right)}$$
Segunda derivada
[src]
/ 2 \
|/ log(atan(2*x)) 2 \ |
||- -------------- + --------------------| |
|| x / 2\ | |
x ___________ |\ \1 + 4*x /*atan(2*x)/ 16 2*log(atan(2*x)) 4 4 |
\/ atan(2*x) *|------------------------------------------ - --------------------- + ---------------- - ------------------------ - -----------------------|
| 2 2 3 2 2 / 2\ |
| x / 2\ x / 2\ 2 x *\1 + 4*x /*atan(2*x)|
\ \1 + 4*x / *atan(2*x) x*\1 + 4*x / *atan (2*x) /
$$\left(- \frac{16}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - \frac{4}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{\left(\frac{2}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x}\right)^{2}}{x^{2}} - \frac{4}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\frac{1}{x}}{\left(2 x \right)}$$
Tercera derivada
[src]
/ 3 / log(atan(2*x)) 2 \ / log(atan(2*x)) 8 2 2 \ \
|/ log(atan(2*x)) 2 \ 6*|- -------------- + --------------------|*|- -------------- + --------------------- + ------------------------ + -----------------------| |
||- -------------- + --------------------| | x / 2\ | | 3 2 2 2 / 2\ | |
|| x / 2\ | \ \1 + 4*x /*atan(2*x)/ | x / 2\ / 2\ 2 x *\1 + 4*x /*atan(2*x)| |
x ___________ |\ \1 + 4*x /*atan(2*x)/ 6*log(atan(2*x)) 96 \ \1 + 4*x / *atan(2*x) x*\1 + 4*x / *atan (2*x) / 12 12 16 32 256*x |
\/ atan(2*x) *|------------------------------------------ - ---------------- + ---------------------- - ------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- + ------------------------- + ------------------------ + ----------------------- + ---------------------|
| 3 4 3 x 3 / 2\ 2 3 2 3 |
| x x / 2\ 2 x *\1 + 4*x /*atan(2*x) 2 / 2\ 2 / 2\ 3 / 2\ / 2\ |
\ \1 + 4*x / *atan (2*x) x *\1 + 4*x / *atan (2*x) x*\1 + 4*x / *atan (2*x) x*\1 + 4*x / *atan(2*x) \1 + 4*x / *atan(2*x)/
$$\left(\frac{256 x}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}{\left(2 x \right)}} + \frac{96}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(2 x \right)}} - \frac{6 \left(\frac{2}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x}\right) \left(\frac{8}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{2}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{2}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{3}}\right)}{x} + \frac{32}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{16}{x \left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(2 x \right)}} + \frac{12}{x^{2} \left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{\left(\frac{2}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x}\right)^{3}}{x^{3}} + \frac{12}{x^{3} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{6 \log{\left(\operatorname{atan}{\left(2 x \right)} \right)}}{x^{4}}\right) \operatorname{atan}^{\frac{1}{x}}{\left(2 x \right)}$$
Gráfico