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:
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Derivada de 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=arctg((cosx)^(uno /x))
- y es igual a arctg(( coseno de x) en el grado (1 dividir por x))
- y es igual a arctg(( coseno de x) en el grado (uno dividir por x))
- y=arctg((cosx)(1/x))
- y=arctgcosx1/x
- y=arctgcosx^1/x
- y=arctg((cosx)^(1 dividir por x))
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Expresiones con funciones
- arctg
- arctg^2(1/x)
- arctg(cos(x))
- arctg(x+cosx)
Derivada de y=arctg((cosx)^(1/x))
Solución
Ha introducido
[src]
/x ________\ atan\\/ cos(x) /
$$\operatorname{atan}{\left(\cos^{\frac{1}{x}}{\left(x \right)} \right)}$$
atan(cos(x)^(1/x))
Primera derivada
[src]
x ________ / log(cos(x)) sin(x) \
\/ cos(x) *|- ----------- - --------|
| 2 x*cos(x)|
\ x /
-------------------------------------
2
-
x
1 + (cos(x))
$$\frac{\left(- \frac{\sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{\log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) \cos^{\frac{1}{x}}{\left(x \right)}}{\cos^{\frac{2}{x}}{\left(x \right)} + 1}$$
Segunda derivada
[src]
/ 2\
| 2 2 -|
| /log(cos(x)) sin(x)\ /log(cos(x)) sin(x)\ x|
| |----------- + ------| 2 2*|----------- + ------| *(cos(x)) |
x ________ | \ x cos(x)/ sin (x) 2*log(cos(x)) 2*sin(x) \ x cos(x)/ |
\/ cos(x) *|-1 + ----------------------- - ------- + ------------- + -------- - -----------------------------------|
| x 2 2 x*cos(x) / 2\ |
| cos (x) x | -| |
| | x| |
\ x*\1 + (cos(x)) / /
--------------------------------------------------------------------------------------------------------------------
/ 2\
| -|
| x|
x*\1 + (cos(x)) /
$$\frac{\left(- \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 1 + \frac{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{2}}{x} - \frac{2 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{2} \cos^{\frac{2}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)} + \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) \cos^{\frac{1}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)}$$
Tercera derivada
[src]
/ 2 \
| / 2 \ 4 2 - / 2 \|
| 3 /log(cos(x)) sin(x)\ | sin (x) 2*log(cos(x)) 2*sin(x)| 3 - 3 - x /log(cos(x)) sin(x)\ | sin (x) 2*log(cos(x)) 2*sin(x)||
| /log(cos(x)) sin(x)\ 3*|----------- + ------|*|1 + ------- - ------------- - --------| /log(cos(x)) sin(x)\ x /log(cos(x)) sin(x)\ x 6*(cos(x)) *|----------- + ------|*|1 + ------- - ------------- - --------||
| |----------- + ------| 3 2 \ x cos(x)/ | 2 2 x*cos(x)| 8*|----------- + ------| *(cos(x)) 8*|----------- + ------| *(cos(x)) \ x cos(x)/ | 2 2 x*cos(x)||
x ________ |3 \ x cos(x)/ 6*log(cos(x)) 2*sin(x) 2*sin (x) 6*sin(x) 3*sin (x) \ cos (x) x / \ x cos(x)/ \ x cos(x)/ \ cos (x) x /|
\/ cos(x) *|- - ----------------------- - ------------- - -------- - --------- - --------- + --------- + ----------------------------------------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------------------------------------------------|
|x 2 3 cos(x) 3 2 2 x 2 / 2\ / 2\ |
| x x cos (x) x *cos(x) x*cos (x) / 2\ | -| | -| |
| | -| 2 | x| | x| |
| 2 | x| x *\1 + (cos(x)) / x*\1 + (cos(x)) / |
\ x *\1 + (cos(x)) / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\
| -|
| x|
x*\1 + (cos(x)) /
$$\frac{\left(- \frac{2 \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{3 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right)}{x} - \frac{6 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right) \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - \frac{2 \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{2 \log{\left(\cos{\left(x \right)} \right)}}{x^{2}}\right) \cos^{\frac{2}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)} + \frac{3 \sin^{2}{\left(x \right)}}{x \cos^{2}{\left(x \right)}} + \frac{3}{x} - \frac{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3}}{x^{2}} + \frac{8 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3} \cos^{\frac{2}{x}}{\left(x \right)}}{x^{2} \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)} - \frac{8 \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\log{\left(\cos{\left(x \right)} \right)}}{x}\right)^{3} \cos^{\frac{4}{x}}{\left(x \right)}}{x^{2} \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)^{2}} - \frac{6 \sin{\left(x \right)}}{x^{2} \cos{\left(x \right)}} - \frac{6 \log{\left(\cos{\left(x \right)} \right)}}{x^{3}}\right) \cos^{\frac{1}{x}}{\left(x \right)}}{x \left(\cos^{\frac{2}{x}}{\left(x \right)} + 1\right)}$$
Gráfico