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:
-
Derivada de 1/(x+3)
-
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
- е^(x/arcsinx)
- е en el grado (x dividir por arc seno de x)
- е(x/arcsinx)
- еx/arcsinx
- е^x/arcsinx
- е^(x dividir por arcsinx)
Derivada de е^(x/arcsinx)
Solución
Ha introducido
[src]
x ------- asin(x) E
$$e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}$$
E^(x/asin(x))
Primera derivada
[src]
x
-------
/ 1 x \ asin(x)
|------- - --------------------|*e
|asin(x) ________ |
| / 2 2 |
\ \/ 1 - x *asin (x)/
$$\left(- \frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{1}{\operatorname{asin}{\left(x \right)}}\right) e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}$$
Segunda derivada
[src]
x
/ 2 2 \ -------
|/ x \ 2 x 2*x | asin(x)
||-1 + -------------------| - ----------- - ----------- - -----------------|*e
|| ________ | ________ 3/2 / 2\ |
|| / 2 | / 2 / 2\ \-1 + x /*asin(x)|
\\ \/ 1 - x *asin(x)/ \/ 1 - x \1 - x / /
--------------------------------------------------------------------------------------
2
asin (x)
$$\frac{\left(- \frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - 1\right)^{2} - \frac{2}{\sqrt{1 - x^{2}}}\right) e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}}{\operatorname{asin}^{2}{\left(x \right)}}$$
Tercera derivada
[src]
/ 3 / 2 \ \
| / x \ / x \ | 2 x 2*x | |
| |-1 + -------------------| 3*|-1 + -------------------|*|----------- + ----------- + -----------------| |
| | ________ | | ________ | | ________ 3/2 / 2\ | | x
| | / 2 | 3 | / 2 | | / 2 / 2\ \-1 + x /*asin(x)| 2 | -------
| \ \/ 1 - x *asin(x)/ 6 4*x 3*x 6*x \ \/ 1 - x *asin(x)/ \\/ 1 - x \1 - x / / 6*x | asin(x)
|- --------------------------- - ----------------- - ----------- - ----------- - -------------------- + ---------------------------------------------------------------------------- + ------------------|*e
| asin(x) / 2\ 3/2 5/2 3/2 asin(x) 2 |
| \-1 + x /*asin(x) / 2\ / 2\ / 2\ 2 / 2\ |
\ \1 - x / \1 - x / \1 - x / *asin (x) \-1 + x / *asin(x)/
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
asin (x)
$$\frac{\left(- \frac{3 x^{3}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} - \frac{4 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}} - \frac{\left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - 1\right)^{3}}{\operatorname{asin}{\left(x \right)}} + \frac{3 \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} - 1\right) \left(\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \frac{2}{\sqrt{1 - x^{2}}}\right)}{\operatorname{asin}{\left(x \right)}} - \frac{6}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right) e^{\frac{x}{\operatorname{asin}{\left(x \right)}}}}{\operatorname{asin}^{2}{\left(x \right)}}$$
Gráfico