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)
-
Derivada de x^-8
-
Derivada de x^2/lnx
-
Derivada de √x+2
-
Expresiones idénticas
- y=arctg*(sinx+cosx)/(sinx-cosx)
- y es igual a arctg multiplicar por ( seno de x más coseno de x) dividir por ( seno de x menos coseno de x)
- y=arctg(sinx+cosx)/(sinx-cosx)
- y=arctgsinx+cosx/sinx-cosx
- y=arctg*(sinx+cosx) dividir por (sinx-cosx)
-
Expresiones semejantes
- y=arctg*(sinx+cosx)/(sinx+cosx)
- y=arctg*(sinx-cosx)/(sinx-cosx)
-
Expresiones con funciones
- arctg
- arctg^2(1/x)
Derivada de y=arctg*(sinx+cosx)/(sinx-cosx)
Solución
Ha introducido
[src]
atan(sin(x) + cos(x)) --------------------- sin(x) - cos(x)
$$\frac{\operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}}$$
atan(sin(x) + cos(x))/(sin(x) - cos(x))
Primera derivada
[src]
-sin(x) + cos(x) (-cos(x) - sin(x))*atan(sin(x) + cos(x)) ------------------------------------------ + ---------------------------------------- / 2\ 2 \1 + (sin(x) + cos(x)) /*(sin(x) - cos(x)) (sin(x) - cos(x))
$$\frac{\left(- \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}} + \frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{\left(\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)}$$
Segunda derivada
[src]
/ 2 \
| 2*(-cos(x) + sin(x)) |
|1 + ----------------------|*(cos(x) + sin(x))
/ 2\ | 2|
| 2*(cos(x) + sin(x)) | 2*(cos(x) + sin(x)) \ 1 + (cos(x) + sin(x)) /
|1 + --------------------|*atan(cos(x) + sin(x)) + ---------------------- - ----------------------------------------------
| 2 | 2 2
\ (-cos(x) + sin(x)) / 1 + (cos(x) + sin(x)) 1 + (cos(x) + sin(x))
--------------------------------------------------------------------------------------------------------------------------
-cos(x) + sin(x)
$$\frac{- \frac{\left(1 + \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} + \left(1 + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}\right) \operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)} + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}}{\sin{\left(x \right)} - \cos{\left(x \right)}}$$
Tercera derivada
[src]
2 2 2 2
6*(cos(x) + sin(x)) 2*(-cos(x) + sin(x)) 8*(-cos(x) + sin(x)) *(cos(x) + sin(x)) / 2\ / 2\ / 2 \
1 - ---------------------- + ---------------------- - ---------------------------------------- | 2*(cos(x) + sin(x)) | | 6*(cos(x) + sin(x)) | 2 | 2*(-cos(x) + sin(x)) |
2 2 2 3*|1 + --------------------| |5 + --------------------|*(cos(x) + sin(x))*atan(cos(x) + sin(x)) 3*(cos(x) + sin(x)) *|1 + ----------------------|
1 + (cos(x) + sin(x)) 1 + (cos(x) + sin(x)) / 2\ | 2 | | 2 | | 2|
\1 + (cos(x) + sin(x)) / \ (-cos(x) + sin(x)) / \ (-cos(x) + sin(x)) / \ 1 + (cos(x) + sin(x)) /
---------------------------------------------------------------------------------------------- - ---------------------------- - ------------------------------------------------------------------ + -------------------------------------------------
2 2 2 / 2\ 2
1 + (cos(x) + sin(x)) 1 + (cos(x) + sin(x)) (-cos(x) + sin(x)) \1 + (cos(x) + sin(x)) /*(-cos(x) + sin(x))
$$\frac{3 \left(1 + \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}} - \frac{3 \left(1 + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} - \frac{\left(5 + \frac{6 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}} + \frac{1 + \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} - \frac{6 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} - \frac{8 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1\right)^{2}}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}$$
Gráfico