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^3)/3
-
Derivada de sqrt(x^2+1)
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Derivada de cos(x)^2
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Derivada de sin(x)/cos(x)
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Expresiones idénticas
- asin(sin(t)/cos(t))
- ar coseno de eno de ( seno de (t) dividir por coseno de (t))
- asinsint/cost
- asin(sin(t) dividir por cos(t))
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Expresiones semejantes
- arcsin(sin(t)/cos(t))
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Expresiones con funciones
- Arcoseno arcsin
- asin(2*x)
- asin(x)^4
- asin(x)/sqrt(1-x^2)+tan(x)*cot((x-1)/(x))
- asin(y^2)
- asin(2*x)^(3)
- Seno sin
- sin(x)/cos(x)
- sin(x)-cos(x)
- sin(x)*sin(x)
- sin(x)/2
- sin(2*x)^(2)
- Coseno cos
- cos(x)^2
- cos(x)^(2)
- cos(x)/(1+sin(x))
- cos(x)/e^x
- cos(2*x-4)
Derivada de asin(sin(t)/cos(t))
Solución
Ha introducido
[src]
/sin(t)\
asin|------|
\cos(t)/
$$\operatorname{asin}{\left(\frac{\sin{\left(t \right)}}{\cos{\left(t \right)}} \right)}$$
asin(sin(t)/cos(t))
Primera derivada
[src]
2
sin (t)
1 + -------
2
cos (t)
-------------------
_____________
/ 2
/ sin (t)
/ 1 - -------
/ 2
\/ cos (t)
$$\frac{\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}{\sqrt{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}}$$
Segunda derivada
[src]
/ 2 \
| sin (t)|
| 1 + -------|
/ 2 \ | 2 |
| sin (t)| | cos (t)|
|1 + -------|*|2 + -----------|*sin(t)
| 2 | | 2 |
\ cos (t)/ | sin (t)|
| 1 - -------|
| 2 |
\ cos (t)/
--------------------------------------
_____________
/ 2
/ sin (t)
/ 1 - ------- *cos(t)
/ 2
\/ cos (t)
$$\frac{\left(2 + \frac{\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}\right) \left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \sin{\left(t \right)}}{\sqrt{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1} \cos{\left(t \right)}}$$
Tercera derivada
[src]
3 2
/ 2 \ / 4 2 \ / 2 \ / 2 \
| sin (t)| | 3*sin (t) 4*sin (t)| | sin (t)| 2 | sin (t)| 2
|1 + -------|*|1 + --------- + ---------| 3*|1 + -------| *sin (t) 4*|1 + -------| *sin (t)
4 2 | 2 | | 4 2 | | 2 | | 2 |
6*sin (t) 8*sin (t) \ cos (t)/ \ cos (t) cos (t) / \ cos (t)/ \ cos (t)/
2 + --------- + --------- + ----------------------------------------- + ------------------------ + ------------------------
4 2 2 2 / 2 \
cos (t) cos (t) sin (t) / 2 \ | sin (t)| 2
1 - ------- | sin (t)| 2 |1 - -------|*cos (t)
2 |1 - -------| *cos (t) | 2 |
cos (t) | 2 | \ cos (t)/
\ cos (t)/
---------------------------------------------------------------------------------------------------------------------------
_____________
/ 2
/ sin (t)
/ 1 - -------
/ 2
\/ cos (t)
$$\frac{\frac{6 \sin^{4}{\left(t \right)}}{\cos^{4}{\left(t \right)}} + \frac{8 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 2 + \frac{4 \left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)^{2} \sin^{2}{\left(t \right)}}{\left(- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \cos^{2}{\left(t \right)}} + \frac{\left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right) \left(\frac{3 \sin^{4}{\left(t \right)}}{\cos^{4}{\left(t \right)}} + \frac{4 \sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)}{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1} + \frac{3 \left(\frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)^{3} \sin^{2}{\left(t \right)}}{\left(- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1\right)^{2} \cos^{2}{\left(t \right)}}}{\sqrt{- \frac{\sin^{2}{\left(t \right)}}{\cos^{2}{\left(t \right)}} + 1}}$$
Gráfico