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 e^-1
-
Derivada de (x^2)'
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Derivada de y
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Derivada de (x^5+1)
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Expresiones idénticas
- y=cos^5x/arcsin8x
- y es igual a coseno de en el grado 5x dividir por arc seno de 8x
- y=cos5x/arcsin8x
- y=cos⁵x/arcsin8x
- y=cos^5x dividir por arcsin8x
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Expresiones con funciones
- Coseno cos
- cos(x)/2
- cosx/lnx
- cos(x)^(1/2)
- cos(x)*log(x)
- cos(x)^(23)
Derivada de y=cos^5x/arcsin8x
Solución
Ha introducido
[src]
5 cos (x) --------- asin(8*x)
$$\frac{\cos^{5}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}}$$
cos(x)^5/asin(8*x)
Primera derivada
[src]
5 4
8*cos (x) 5*cos (x)*sin(x)
- ------------------------- - ----------------
___________ asin(8*x)
/ 2 2
\/ 1 - 64*x *asin (8*x)
$$- \frac{5 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} - \frac{8 \cos^{5}{\left(x \right)}}{\sqrt{1 - 64 x^{2}} \operatorname{asin}^{2}{\left(8 x \right)}}$$
Segunda derivada
[src]
/ 2 / 1 4*x \ \
| 128*cos (x)*|---------------------- + --------------| |
| |/ 2\ 3/2| |
| |\-1 + 64*x /*asin(8*x) / 2\ | |
3 | 2 2 \ \1 - 64*x / / 80*cos(x)*sin(x) |
cos (x)*|- 5*cos (x) + 20*sin (x) - ----------------------------------------------------- + ------------------------|
| asin(8*x) ___________ |
| / 2 |
\ \/ 1 - 64*x *asin(8*x)/
---------------------------------------------------------------------------------------------------------------------
asin(8*x)
$$\frac{\left(- \frac{128 \left(\frac{4 x}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(64 x^{2} - 1\right) \operatorname{asin}{\left(8 x \right)}}\right) \cos^{2}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} + 20 \sin^{2}{\left(x \right)} - 5 \cos^{2}{\left(x \right)} + \frac{80 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - 64 x^{2}} \operatorname{asin}{\left(8 x \right)}}\right) \cos^{3}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 | 1 6 192*x 48*x | 2 / 1 4*x \ |
| 512*cos (x)*|-------------- + ------------------------- + -------------- - -----------------------| 1920*cos (x)*|---------------------- + --------------|*sin(x)|
| | 3/2 3/2 5/2 2 | |/ 2\ 3/2| |
| |/ 2\ / 2\ 2 / 2\ / 2\ | / 2 2 \ |\-1 + 64*x /*asin(8*x) / 2\ | |
2 | / 2 2 \ \\1 - 64*x / \1 - 64*x / *asin (8*x) \1 - 64*x / \-1 + 64*x / *asin(8*x)/ 120*\- cos (x) + 4*sin (x)/*cos(x) \ \1 - 64*x / / |
cos (x)*|- 5*\- 13*cos (x) + 12*sin (x)/*sin(x) - --------------------------------------------------------------------------------------------------- - ---------------------------------- + -------------------------------------------------------------|
| asin(8*x) ___________ asin(8*x) |
| / 2 |
\ \/ 1 - 64*x *asin(8*x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
asin(8*x)
$$\frac{\left(\frac{1920 \left(\frac{4 x}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(64 x^{2} - 1\right) \operatorname{asin}{\left(8 x \right)}}\right) \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} - 5 \left(12 \sin^{2}{\left(x \right)} - 13 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} - \frac{512 \left(\frac{192 x^{2}}{\left(1 - 64 x^{2}\right)^{\frac{5}{2}}} - \frac{48 x}{\left(64 x^{2} - 1\right)^{2} \operatorname{asin}{\left(8 x \right)}} + \frac{1}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 64 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(8 x \right)}}\right) \cos^{3}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}} - \frac{120 \left(4 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{\sqrt{1 - 64 x^{2}} \operatorname{asin}{\left(8 x \right)}}\right) \cos^{2}{\left(x \right)}}{\operatorname{asin}{\left(8 x \right)}}$$
Gráfico