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^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=arctg^ cinco (e^arcsinx^ dos)
- y es igual a arctg en el grado 5(e en el grado arc seno de x al cuadrado )
- y es igual a arctg en el grado cinco (e en el grado arc seno de x en el grado dos)
- y=arctg5(earcsinx2)
- y=arctg5earcsinx2
- y=arctg⁵(e^arcsinx²)
- y=arctg en el grado 5(e en el grado arcsinx en el grado 2)
- y=arctg^5e^arcsinx^2
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Expresiones con funciones
- arctg
- arctg^2(1/x)
Derivada de y=arctg^5(e^arcsinx^2)
Solución
Ha introducido
[src]
/ 2 \
5| asin (x)|
atan \E /
$$\operatorname{atan}^{5}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}$$
atan(E^(asin(x)^2))^5
Primera derivada
[src]
/ 2 \ 2
4| asin (x)| asin (x)
10*atan \E /*asin(x)*e
-------------------------------------
________ / 2 \
/ 2 | 2*asin (x)|
\/ 1 - x *\1 + e /
$$\frac{10 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}{\left(x \right)} \operatorname{atan}^{4}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\sqrt{1 - x^{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)}$$
Segunda derivada
[src]
/ / 2 \ / 2 \ / 2 \ 2 / 2 \ 2 \
/ 2 \ | | asin (x)| 2 | asin (x)| | asin (x)| 2 asin (x) 2 | asin (x)| 2*asin (x)| 2
3| asin (x)| | atan\E / 2*asin (x)*atan\E / x*asin(x)*atan\E / 8*asin (x)*e 4*asin (x)*atan\E /*e | asin (x)
10*atan \E /*|- --------------- - -------------------------- + ------------------------- - --------------------------- + --------------------------------------|*e
| 2 2 3/2 / 2 \ / 2 \ |
| -1 + x -1 + x / 2\ | 2*asin (x)| / 2\ | 2*asin (x)| / 2\ |
\ \1 - x / \1 + e /*\-1 + x / \1 + e /*\-1 + x / /
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2
2*asin (x)
1 + e
$$\frac{10 \left(\frac{x \operatorname{asin}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{x^{2} - 1} - \frac{\operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{x^{2} - 1} + \frac{4 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right) \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} - \frac{8 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)}}{\left(x^{2} - 1\right) \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)}\right) e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{atan}^{3}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1}$$
Tercera derivada
[src]
/ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ 2 / 2 \ 2 / 2 \ 2 / 2 \ 2 / 2 \ 2 / 2 \ 2 / 2 \ 2 / 2 \ 2 / 2 \ 2 \
/ 2 \ | 2| asin (x)| 3 2| asin (x)| 2| asin (x)| 2 2| asin (x)| 2 2| asin (x)| 3 2*asin (x) 3 | asin (x)| 3*asin (x) 3 2| asin (x)| 2*asin (x) 2| asin (x)| 2*asin (x) | asin (x)| asin (x) 3 2| asin (x)| 4*asin (x) 3 | asin (x)| asin (x) 2 2| asin (x)| 2*asin (x) 2 | asin (x)| asin (x)| 2
2| asin (x)| |3*x*atan \E / 4*asin (x)*atan \E / 7*atan \E /*asin(x) 3*x *atan \E /*asin(x) 6*x*asin (x)*atan \E / 48*asin (x)*e 96*asin (x)*atan\E /*e 32*asin (x)*atan \E /*e 12*atan \E /*asin(x)*e 24*asin(x)*atan\E /*e 32*asin (x)*atan \E /*e 48*asin (x)*atan\E /*e 12*x*asin (x)*atan \E /*e 24*x*asin (x)*atan\E /*e | asin (x)
10*atan \E /*|-------------------- + --------------------------- + -------------------------- + ----------------------------- + ----------------------------- + ------------------------------ - --------------------------------------- - ---------------------------------------- - --------------------------------------- + ------------------------------------ + ---------------------------------------- + ------------------------------------- - ------------------------------------------ + ---------------------------------------|*e
| 2 3/2 3/2 5/2 2 2 2 3/2 / 2 \ 3/2 / 2 \ 3/2 / 2 \ 2 3/2 / 2 \ / 2 \ 2 / 2 \ 2 |
| / 2\ / 2\ / 2\ / 2\ / 2\ 3/2 / 2 \ 3/2 / 2 \ / 2\ | 2*asin (x)| / 2\ | 2*asin (x)| / 2\ | 2*asin (x)| 3/2 / 2 \ / 2\ | 2*asin (x)| | 2*asin (x)| / 2\ | 2*asin (x)| / 2\ |
| \-1 + x / \1 - x / \1 - x / \1 - x / \-1 + x / / 2\ | 2*asin (x)| / 2\ | 2*asin (x)| \1 - x / *\1 + e / \1 - x / *\1 + e / \1 - x / *\1 + e / / 2\ | 2*asin (x)| \1 - x / *\1 + e / \1 + e /*\-1 + x / \1 + e /*\-1 + x / |
\ \1 - x / *\1 + e / \1 - x / *\1 + e / \1 - x / *\1 + e / /
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2
2*asin (x)
1 + e
$$\frac{10 \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{12 x e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{24 x e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{2}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(x^{2} - 1\right)^{2} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{4 \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{7 \operatorname{asin}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{32 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} - \frac{12 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{48 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{24 e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)} + \frac{32 e^{4 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)^{2}} - \frac{96 e^{3 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)} \operatorname{atan}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)^{2}} + \frac{48 e^{2 \operatorname{asin}^{2}{\left(x \right)}} \operatorname{asin}^{3}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1\right)^{2}}\right) e^{\operatorname{asin}^{2}{\left(x \right)}} \operatorname{atan}^{2}{\left(e^{\operatorname{asin}^{2}{\left(x \right)}} \right)}}{e^{2 \operatorname{asin}^{2}{\left(x \right)}} + 1}$$
Gráfico