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 e^-1
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Derivada de (x^2)'
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Derivada de y
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Derivada de 16/x
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Expresiones idénticas
- y=sin^ ocho (6x)*arctg dos x^2
- y es igual a seno de en el grado 8(6x) multiplicar por arctg2x al cuadrado
- y es igual a seno de en el grado ocho (6x) multiplicar por arctg dos x al cuadrado
- y=sin8(6x)*arctg2x2
- y=sin86x*arctg2x2
- y=sin⁸(6x)*arctg2x²
- y=sin en el grado 8(6x)*arctg2x en el grado 2
- y=sin^8(6x)arctg2x^2
- y=sin8(6x)arctg2x2
- y=sin86xarctg2x2
- y=sin^86xarctg2x^2
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Expresiones con funciones
- Seno sin
- sin(3*x+2)
- sin^4(x)
- sin^3x
- sin(x)^3
- sin(x)^(1/2)
Derivada de y=sin^8(6x)*arctg2x^2
Solución
Ha introducido
[src]
8 2 sin (6*x)*atan (2*x)
$$\sin^{8}{\left(6 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}$$
sin(6*x)^8*atan(2*x)^2
Primera derivada
[src]
8
4*sin (6*x)*atan(2*x) 2 7
--------------------- + 48*atan (2*x)*sin (6*x)*cos(6*x)
2
1 + 4*x
$$48 \sin^{7}{\left(6 x \right)} \cos{\left(6 x \right)} \operatorname{atan}^{2}{\left(2 x \right)} + \frac{4 \sin^{8}{\left(6 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada
[src]
/ 2 \
6 | 2 / 2 2 \ sin (6*x)*(-1 + 4*x*atan(2*x)) 48*atan(2*x)*cos(6*x)*sin(6*x)|
8*sin (6*x)*|- 36*atan (2*x)*\sin (6*x) - 7*cos (6*x)/ - ------------------------------ + ------------------------------|
| 2 2 |
| / 2\ 1 + 4*x |
\ \1 + 4*x / /
$$8 \left(- 36 \left(\sin^{2}{\left(6 x \right)} - 7 \cos^{2}{\left(6 x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} + \frac{48 \sin{\left(6 x \right)} \cos{\left(6 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{\left(4 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(6 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{6}{\left(6 x \right)}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 | 6*x 16*x *atan(2*x) | |
|sin (6*x)*|-------- - --------------- + atan(2*x)| |
| | 2 2 | 2 / 2 2 \ |
5 | \1 + 4*x 1 + 4*x / 2 / 2 2 \ 36*sin (6*x)*(-1 + 4*x*atan(2*x))*cos(6*x) 108*\sin (6*x) - 7*cos (6*x)/*atan(2*x)*sin(6*x)|
-32*sin (6*x)*|-------------------------------------------------- + 108*atan (2*x)*\- 21*cos (6*x) + 11*sin (6*x)/*cos(6*x) + ------------------------------------------ + ------------------------------------------------|
| 2 2 2 |
| / 2\ / 2\ 1 + 4*x |
\ \1 + 4*x / \1 + 4*x / /
$$- 32 \left(108 \left(11 \sin^{2}{\left(6 x \right)} - 21 \cos^{2}{\left(6 x \right)}\right) \cos{\left(6 x \right)} \operatorname{atan}^{2}{\left(2 x \right)} + \frac{108 \left(\sin^{2}{\left(6 x \right)} - 7 \cos^{2}{\left(6 x \right)}\right) \sin{\left(6 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{36 \left(4 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(6 x \right)} \cos{\left(6 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{\left(- \frac{16 x^{2} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{6 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \sin^{3}{\left(6 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{5}{\left(6 x \right)}$$
Gráfico