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^4 tres x*arctg2x^3
- y es igual a seno de en el grado 43x multiplicar por arctg2x al cubo
- y es igual a seno de en el grado 4 tres x multiplicar por arctg2x al cubo
- y=sin43x*arctg2x3
- y=sin⁴3x*arctg2x³
- y=sin en el grado 43x*arctg2x en el grado 3
- y=sin^43xarctg2x^3
- y=sin43xarctg2x3
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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^43x*arctg2x^3
Solución
Ha introducido
[src]
4 3 sin (3*x)*atan (2*x)
$$\sin^{4}{\left(3 x \right)} \operatorname{atan}^{3}{\left(2 x \right)}$$
sin(3*x)^4*atan(2*x)^3
Primera derivada
[src]
2 4
6*atan (2*x)*sin (3*x) 3 3
---------------------- + 12*atan (2*x)*sin (3*x)*cos(3*x)
2
1 + 4*x
$$12 \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \sin^{4}{\left(3 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada
[src]
/ 2 \
2 | 2 / 2 2 \ 2*sin (3*x)*(-1 + 2*x*atan(2*x)) 12*atan(2*x)*cos(3*x)*sin(3*x)|
12*sin (3*x)*|- 3*atan (2*x)*\sin (3*x) - 3*cos (3*x)/ - -------------------------------- + ------------------------------|*atan(2*x)
| 2 2 |
| / 2\ 1 + 4*x |
\ \1 + 4*x / /
$$12 \left(- 3 \left(\sin^{2}{\left(3 x \right)} - 3 \cos^{2}{\left(3 x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} + \frac{12 \sin{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{2 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(3 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{2}{\left(3 x \right)} \operatorname{atan}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \ | 3 | 1 2 12*x*atan(2*x) 16*x *atan (2*x)| | | 2*sin (3*x)*|-------- - atan (2*x) - -------------- + ----------------| | | | 2 2 2 | 2 / 2 2 \ 2 | | 3 / 2 2 \ \1 + 4*x 1 + 4*x 1 + 4*x / 27*atan (2*x)*\sin (3*x) - 3*cos (3*x)/*sin(3*x) 36*sin (3*x)*(-1 + 2*x*atan(2*x))*atan(2*x)*cos(3*x)| 24*|- 9*atan (2*x)*\- 3*cos (3*x) + 5*sin (3*x)/*cos(3*x) + ----------------------------------------------------------------------- - ------------------------------------------------ - ----------------------------------------------------|*sin(3*x) | 2 2 2 | | / 2\ 1 + 4*x / 2\ | \ \1 + 4*x / \1 + 4*x / /
$$24 \left(- 9 \left(5 \sin^{2}{\left(3 x \right)} - 3 \cos^{2}{\left(3 x \right)}\right) \cos{\left(3 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} - \frac{27 \left(\sin^{2}{\left(3 x \right)} - 3 \cos^{2}{\left(3 x \right)}\right) \sin{\left(3 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{36 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \sin^{3}{\left(3 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin{\left(3 x \right)}$$
Gráfico