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 -2*y
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Derivada de 3^2*x
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Derivada de 2*x+8/x
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Derivada de -1/y
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Expresiones idénticas
- y=arctg^ dos (cos3x)
- y es igual a arctg al cuadrado ( coseno de 3x)
- y es igual a arctg en el grado dos ( coseno de 3x)
- y=arctg2(cos3x)
- y=arctg2cos3x
- y=arctg²(cos3x)
- y=arctg en el grado 2(cos3x)
- y=arctg^2cos3x
Derivada de y=arctg^2(cos3x)
Solución
Ha introducido
[src]
2 atan (cos(3*x))
$$\operatorname{atan}^{2}{\left(\cos{\left(3 x \right)} \right)}$$
atan(cos(3*x))^2
Primera derivada
[src]
-6*atan(cos(3*x))*sin(3*x)
--------------------------
2
1 + cos (3*x)
$$- \frac{6 \sin{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 \
| sin (3*x) 2*sin (3*x)*atan(cos(3*x))*cos(3*x)|
18*|------------- - atan(cos(3*x))*cos(3*x) - -----------------------------------|
| 2 2 |
\1 + cos (3*x) 1 + cos (3*x) /
----------------------------------------------------------------------------------
2
1 + cos (3*x)
$$\frac{18 \left(- \cos{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)} - \frac{2 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1} + \frac{\sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)} + 1}\right)}{\cos^{2}{\left(3 x \right)} + 1}$$
Tercera derivada
[src]
/ 2 2 2 2 2 \
| 3*cos(3*x) 6*cos (3*x)*atan(cos(3*x)) 2*sin (3*x)*atan(cos(3*x)) 6*sin (3*x)*cos(3*x) 8*cos (3*x)*sin (3*x)*atan(cos(3*x)) |
54*|------------- - -------------------------- + -------------------------- + -------------------- - ------------------------------------ + atan(cos(3*x))|*sin(3*x)
| 2 2 2 2 2 |
|1 + cos (3*x) 1 + cos (3*x) 1 + cos (3*x) / 2 \ / 2 \ |
\ \1 + cos (3*x)/ \1 + cos (3*x)/ /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + cos (3*x)
$$\frac{54 \left(\operatorname{atan}{\left(\cos{\left(3 x \right)} \right)} + \frac{2 \sin^{2}{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1} - \frac{6 \cos^{2}{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\cos^{2}{\left(3 x \right)} + 1} + \frac{3 \cos{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)} + 1} - \frac{8 \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)} \operatorname{atan}{\left(\cos{\left(3 x \right)} \right)}}{\left(\cos^{2}{\left(3 x \right)} + 1\right)^{2}} + \frac{6 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{\left(\cos^{2}{\left(3 x \right)} + 1\right)^{2}}\right) \sin{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)} + 1}$$
Gráfico