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^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=x*arctg^ dos (sin2x)
- y es igual a x multiplicar por arctg al cuadrado ( seno de 2x)
- y es igual a x multiplicar por arctg en el grado dos ( seno de 2x)
- y=x*arctg2(sin2x)
- y=x*arctg2sin2x
- y=x*arctg²(sin2x)
- y=x*arctg en el grado 2(sin2x)
- y=xarctg^2(sin2x)
- y=xarctg2(sin2x)
- y=xarctg2sin2x
- y=xarctg^2sin2x
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Expresiones con funciones
- arctg
- arctg^2(1/x)
Derivada de y=x*arctg^2(sin2x)
Solución
Ha introducido
[src]
2 x*atan (sin(2*x))
$$x \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \right)}$$
x*atan(sin(2*x))^2
Primera derivada
[src]
2 4*x*atan(sin(2*x))*cos(2*x)
atan (sin(2*x)) + ---------------------------
2
1 + sin (2*x)
$$\frac{4 x \cos{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \operatorname{atan}^{2}{\left(\sin{\left(2 x \right)} \right)}$$
Segunda derivada
[src]
/ / 2 2 \\
| | cos (2*x) 2*cos (2*x)*atan(sin(2*x))*sin(2*x)||
8*|atan(sin(2*x))*cos(2*x) - x*|atan(sin(2*x))*sin(2*x) - ------------- + -----------------------------------||
| | 2 2 ||
\ \ 1 + sin (2*x) 1 + sin (2*x) //
---------------------------------------------------------------------------------------------------------------
2
1 + sin (2*x)
$$\frac{8 \left(- x \left(\sin{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} + \frac{2 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{\cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1}\right) + \cos{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}\right)}{\sin^{2}{\left(2 x \right)} + 1}$$
3-я производная
[src]
/ 2 / 2 2 2 2 2 \ 2 \
| 3*cos (2*x) | 3*sin(2*x) 6*sin (2*x)*atan(sin(2*x)) 2*cos (2*x)*atan(sin(2*x)) 6*cos (2*x)*sin(2*x) 8*cos (2*x)*sin (2*x)*atan(sin(2*x)) | 6*cos (2*x)*atan(sin(2*x))*sin(2*x)|
-8*|- ------------- + 3*atan(sin(2*x))*sin(2*x) + 2*x*|------------- - -------------------------- + -------------------------- + -------------------- - ------------------------------------ + atan(sin(2*x))|*cos(2*x) + -----------------------------------|
| 2 | 2 2 2 2 2 | 2 |
| 1 + sin (2*x) |1 + sin (2*x) 1 + sin (2*x) 1 + sin (2*x) / 2 \ / 2 \ | 1 + sin (2*x) |
\ \ \1 + sin (2*x)/ \1 + sin (2*x)/ / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + sin (2*x)
$$- \frac{8 \left(2 x \left(\operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} - \frac{6 \sin^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{3 \sin{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{2 \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{8 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{3 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1}\right)}{\sin^{2}{\left(2 x \right)} + 1}$$
Tercera derivada
[src]
/ 2 / 2 2 2 2 2 \ 2 \
| 3*cos (2*x) | 3*sin(2*x) 6*sin (2*x)*atan(sin(2*x)) 2*cos (2*x)*atan(sin(2*x)) 6*cos (2*x)*sin(2*x) 8*cos (2*x)*sin (2*x)*atan(sin(2*x)) | 6*cos (2*x)*atan(sin(2*x))*sin(2*x)|
-8*|- ------------- + 3*atan(sin(2*x))*sin(2*x) + 2*x*|------------- - -------------------------- + -------------------------- + -------------------- - ------------------------------------ + atan(sin(2*x))|*cos(2*x) + -----------------------------------|
| 2 | 2 2 2 2 2 | 2 |
| 1 + sin (2*x) |1 + sin (2*x) 1 + sin (2*x) 1 + sin (2*x) / 2 \ / 2 \ | 1 + sin (2*x) |
\ \ \1 + sin (2*x)/ \1 + sin (2*x)/ / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + sin (2*x)
$$- \frac{8 \left(2 x \left(\operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} - \frac{6 \sin^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{3 \sin{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1} + \frac{2 \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{8 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(\sin^{2}{\left(2 x \right)} + 1\right)^{2}}\right) \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)} + \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)} \operatorname{atan}{\left(\sin{\left(2 x \right)} \right)}}{\sin^{2}{\left(2 x \right)} + 1} - \frac{3 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)} + 1}\right)}{\sin^{2}{\left(2 x \right)} + 1}$$
Gráfico