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:
-
Derivada de x^-7
- Derivada de i*n*x
-
Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- y=arctg^ tres (cos(2x))
- y es igual a arctg al cubo ( coseno de (2x))
- y es igual a arctg en el grado tres ( coseno de (2x))
- y=arctg3(cos(2x))
- y=arctg3cos2x
- y=arctg³(cos(2x))
- y=arctg en el grado 3(cos(2x))
- y=arctg^3cos2x
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Expresiones con funciones
- arctg
- arctg^2(1/x)
- Coseno cos
- cos(x)+49
- cos(x-1)
- cos(sqrt(x)+3*x)
- cos(x)*x^3
- cos(asin(x))
Derivada de y=arctg^3(cos(2x))
Solución
Ha introducido
[src]
3 atan (cos(2*x))
$$\operatorname{atan}^{3}{\left(\cos{\left(2 x \right)} \right)}$$
atan(cos(2*x))^3
Primera derivada
[src]
2
-6*atan (cos(2*x))*sin(2*x)
---------------------------
2
1 + cos (2*x)
$$- \frac{6 \sin{\left(2 x \right)} \operatorname{atan}^{2}{\left(\cos{\left(2 x \right)} \right)}}{\cos^{2}{\left(2 x \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 \
| 2*sin (2*x) 2*sin (2*x)*atan(cos(2*x))*cos(2*x)|
12*|-atan(cos(2*x))*cos(2*x) + ------------- - -----------------------------------|*atan(cos(2*x))
| 2 2 |
\ 1 + cos (2*x) 1 + cos (2*x) /
--------------------------------------------------------------------------------------------------
2
1 + cos (2*x)
$$\frac{12 \left(- \cos{\left(2 x \right)} \operatorname{atan}{\left(\cos{\left(2 x \right)} \right)} - \frac{2 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)} \operatorname{atan}{\left(\cos{\left(2 x \right)} \right)}}{\cos^{2}{\left(2 x \right)} + 1} + \frac{2 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} + 1}\right) \operatorname{atan}{\left(\cos{\left(2 x \right)} \right)}}{\cos^{2}{\left(2 x \right)} + 1}$$
Tercera derivada
[src]
/ 2 2 2 2 2 2 2 2 2 \
| 2 2*sin (2*x) 6*atan (cos(2*x))*cos (2*x) 2*atan (cos(2*x))*sin (2*x) 6*atan(cos(2*x))*cos(2*x) 8*atan (cos(2*x))*cos (2*x)*sin (2*x) 12*sin (2*x)*atan(cos(2*x))*cos(2*x)|
24*|atan (cos(2*x)) - ---------------- - --------------------------- + --------------------------- + ------------------------- - ------------------------------------- + ------------------------------------|*sin(2*x)
| 2 2 2 2 2 2 |
| / 2 \ 1 + cos (2*x) 1 + cos (2*x) 1 + cos (2*x) / 2 \ / 2 \ |
\ \1 + cos (2*x)/ \1 + cos (2*x)/ \1 + cos (2*x)/ /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + cos (2*x)
$$\frac{24 \left(\operatorname{atan}^{2}{\left(\cos{\left(2 x \right)} \right)} + \frac{2 \sin^{2}{\left(2 x \right)} \operatorname{atan}^{2}{\left(\cos{\left(2 x \right)} \right)}}{\cos^{2}{\left(2 x \right)} + 1} - \frac{6 \cos^{2}{\left(2 x \right)} \operatorname{atan}^{2}{\left(\cos{\left(2 x \right)} \right)}}{\cos^{2}{\left(2 x \right)} + 1} + \frac{6 \cos{\left(2 x \right)} \operatorname{atan}{\left(\cos{\left(2 x \right)} \right)}}{\cos^{2}{\left(2 x \right)} + 1} - \frac{8 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}^{2}{\left(\cos{\left(2 x \right)} \right)}}{\left(\cos^{2}{\left(2 x \right)} + 1\right)^{2}} + \frac{12 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)} \operatorname{atan}{\left(\cos{\left(2 x \right)} \right)}}{\left(\cos^{2}{\left(2 x \right)} + 1\right)^{2}} - \frac{2 \sin^{2}{\left(2 x \right)}}{\left(\cos^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \sin{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)} + 1}$$
Gráfico