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 1/(x+1)^2
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Derivada de (x+3)/(x-2)
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Derivada de (x+4)^2*(x+1)+9
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Derivada de e^(2-x)
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Expresiones idénticas
- y=arctg^ tres (2x)*cos8x^ cinco
- y es igual a arctg al cubo (2x) multiplicar por coseno de 8x en el grado 5
- y es igual a arctg en el grado tres (2x) multiplicar por coseno de 8x en el grado cinco
- y=arctg3(2x)*cos8x5
- y=arctg32x*cos8x5
- y=arctg³(2x)*cos8x⁵
- y=arctg en el grado 3(2x)*cos8x en el grado 5
- y=arctg^3(2x)cos8x^5
- y=arctg3(2x)cos8x5
- y=arctg32xcos8x5
- y=arctg^32xcos8x^5
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Expresiones con funciones
- arctg
- arctg^3*4x*3^sinx
- arctg(sqrt(x))
- arctg(cos(x))
- arctg(x+cosx)
- arctg^2(1/x)
Derivada de y=arctg^3(2x)*cos8x^5
Solución
Ha introducido
[src]
3 5 atan (2*x)*cos (8*x)
$$\cos^{5}{\left(8 x \right)} \operatorname{atan}^{3}{\left(2 x \right)}$$
atan(2*x)^3*cos(8*x)^5
Primera derivada
[src]
2 5
3 4 6*atan (2*x)*cos (8*x)
- 40*atan (2*x)*cos (8*x)*sin(8*x) + ----------------------
2
1 + 4*x
$$- 40 \sin{\left(8 x \right)} \cos^{4}{\left(8 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \cos^{5}{\left(8 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada
[src]
/ 2 \
3 | 2 / 2 2 \ 3*cos (8*x)*(-1 + 2*x*atan(2*x)) 60*atan(2*x)*cos(8*x)*sin(8*x)|
8*cos (8*x)*|40*atan (2*x)*\- cos (8*x) + 4*sin (8*x)/ - -------------------------------- - ------------------------------|*atan(2*x)
| 2 2 |
| / 2\ 1 + 4*x |
\ \1 + 4*x / /
$$8 \left(40 \left(4 \sin^{2}{\left(8 x \right)} - \cos^{2}{\left(8 x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} - \frac{60 \sin{\left(8 x \right)} \cos{\left(8 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{3 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \cos^{2}{\left(8 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \cos^{3}{\left(8 x \right)} \operatorname{atan}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| 3 | 1 2 12*x*atan(2*x) 16*x *atan (2*x)| |
| 3*cos (8*x)*|-------- - atan (2*x) - -------------- + ----------------| |
| | 2 2 2 | 2 / 2 2 \ 2 |
2 | 3 / 2 2 \ \1 + 4*x 1 + 4*x 1 + 4*x / 360*atan (2*x)*\- cos (8*x) + 4*sin (8*x)/*cos(8*x) 180*cos (8*x)*(-1 + 2*x*atan(2*x))*atan(2*x)*sin(8*x)|
16*cos (8*x)*|- 160*atan (2*x)*\- 13*cos (8*x) + 12*sin (8*x)/*sin(8*x) + ----------------------------------------------------------------------- + --------------------------------------------------- + -----------------------------------------------------|
| 2 2 2 |
| / 2\ 1 + 4*x / 2\ |
\ \1 + 4*x / \1 + 4*x / /
$$16 \left(- 160 \left(12 \sin^{2}{\left(8 x \right)} - 13 \cos^{2}{\left(8 x \right)}\right) \sin{\left(8 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{360 \left(4 \sin^{2}{\left(8 x \right)} - \cos^{2}{\left(8 x \right)}\right) \cos{\left(8 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{180 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin{\left(8 x \right)} \cos^{2}{\left(8 x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{3 \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \cos^{3}{\left(8 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \cos^{2}{\left(8 x \right)}$$
Gráfico