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 -5*tan(2*t)-4*cot(4*t)
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Derivada de (3x+6)^2
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Derivada de 3^(x*x)
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Derivada de 2*x-8/x
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Expresiones idénticas
- y=arcctg(cos(x)/x)
- y es igual a arcctg( coseno de (x) dividir por x)
- y=arcctgcosx/x
- y=arcctg(cos(x) dividir por x)
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Expresiones semejantes
- y=arcctg(cosx/x)
Derivada de y=arcctg(cos(x)/x)
Solución
Ha introducido
[src]
/cos(x)\
acot|------|
\ x /
$$\operatorname{acot}{\left(\frac{\cos{\left(x \right)}}{x} \right)}$$
acot(cos(x)/x)
Primera derivada
[src]
/ sin(x) cos(x)\
-|- ------ - ------|
| x 2 |
\ x /
---------------------
2
cos (x)
1 + -------
2
x
$$- \frac{- \frac{\sin{\left(x \right)}}{x} - \frac{\cos{\left(x \right)}}{x^{2}}}{1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}}$$
Segunda derivada
[src]
2
/cos(x) \
2*|------ + sin(x)| *cos(x)
2*sin(x) 2*cos(x) \ x /
- -------- - -------- + --------------------------- + cos(x)
x 2 / 2 \
x 2 | cos (x)|
x *|1 + -------|
| 2 |
\ x /
------------------------------------------------------------
/ 2 \
| cos (x)|
x*|1 + -------|
| 2 |
\ x /
$$\frac{\cos{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x} - \frac{2 \cos{\left(x \right)}}{x^{2}} + \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right)^{2} \cos{\left(x \right)}}{x^{2} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)}}{x \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)}$$
Tercera derivada
[src]
/ 2 \
/cos(x) \ | 2 2 3*cos (x) 4*cos(x)*sin(x)| 3 /cos(x) \ / 2*sin(x) 2*cos(x)\
2*|------ + sin(x)|*|sin (x) - cos (x) + --------- + ---------------| /cos(x) \ 2 4*|------ + sin(x)|*|-cos(x) + -------- + --------|*cos(x)
\ x / | 2 x | 8*|------ + sin(x)| *cos (x) \ x / | x 2 |
3*cos(x) 6*cos(x) 6*sin(x) \ x / \ x / \ x /
-sin(x) - -------- + -------- + -------- - --------------------------------------------------------------------- + ---------------------------- - ----------------------------------------------------------
x 3 2 / 2 \ 2 / 2 \
x x 2 | cos (x)| / 2 \ 2 | cos (x)|
x *|1 + -------| 4 | cos (x)| x *|1 + -------|
| 2 | x *|1 + -------| | 2 |
\ x / | 2 | \ x /
\ x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 \
| cos (x)|
x*|1 + -------|
| 2 |
\ x /
$$\frac{- \sin{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x} + \frac{6 \sin{\left(x \right)}}{x^{2}} - \frac{4 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \left(- \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{2 \cos{\left(x \right)}}{x^{2}}\right) \cos{\left(x \right)}}{x^{2} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)} - \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{3 \cos^{2}{\left(x \right)}}{x^{2}}\right)}{x^{2} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)} + \frac{6 \cos{\left(x \right)}}{x^{3}} + \frac{8 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right)^{3} \cos^{2}{\left(x \right)}}{x^{4} \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)^{2}}}{x \left(1 + \frac{\cos^{2}{\left(x \right)}}{x^{2}}\right)}$$
Gráfico