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 x*acos(x)
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Derivada de x^(1/5)
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Derivada de sin(x)*cos(x)
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Derivada de x*2
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Expresiones idénticas
- y=sinx^ cuatro * tres x*arctg2x^3
- y es igual a seno de x en el grado 4 multiplicar por 3x multiplicar por arctg2x al cubo
- y es igual a seno de x en el grado cuatro multiplicar por tres x multiplicar por arctg2x al cubo
- y=sinx4*3x*arctg2x3
- y=sinx⁴*3x*arctg2x³
- y=sinx en el grado 4*3x*arctg2x en el grado 3
- y=sinx^43xarctg2x^3
- y=sinx43xarctg2x3
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Expresiones con funciones
- sinx
- sinx/1+cosx
- sinx*e^x
- sinx+3
- sinx+2
- sinx^x
Derivada de y=sinx^4*3x*arctg2x^3
Solución
Ha introducido
[src]
4 3 sin (x)*3*x*atan (2*x)
$$x 3 \sin^{4}{\left(x \right)} \operatorname{atan}^{3}{\left(2 x \right)}$$
((sin(x)^4*3)*x)*atan(2*x)^3
Primera derivada
[src]
2 4
3 / 4 3 \ 18*x*atan (2*x)*sin (x)
atan (2*x)*\sin (x)*3 + 12*x*sin (x)*cos(x)/ + -----------------------
2
1 + 4*x
$$\frac{18 x \sin^{4}{\left(x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \left(12 x \sin^{3}{\left(x \right)} \cos{\left(x \right)} + 3 \sin^{4}{\left(x \right)}\right) \operatorname{atan}^{3}{\left(2 x \right)}$$
Segunda derivada
[src]
/ 2 \
2 | 2 / / 2 2 \ \ 6*x*sin (x)*(-1 + 2*x*atan(2*x)) 3*(4*x*cos(x) + sin(x))*atan(2*x)*sin(x)|
12*sin (x)*|- atan (2*x)*\x*\sin (x) - 3*cos (x)/ - 2*cos(x)*sin(x)/ - -------------------------------- + ----------------------------------------|*atan(2*x)
| 2 2 |
| / 2\ 1 + 4*x |
\ \1 + 4*x / /
$$12 \left(- \frac{6 x \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \left(x \left(\sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} + \frac{3 \left(4 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}\right) \sin^{2}{\left(x \right)} \operatorname{atan}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \ | 3 | 1 2 12*x*atan(2*x) 16*x *atan (2*x)| | | 12*x*sin (x)*|-------- - atan (2*x) - -------------- + ----------------| | | 2 / / 2 2 \ \ | 2 2 2 | 2 | | 3 / / 2 2 \ / 2 2 \ \ 18*atan (2*x)*\x*\sin (x) - 3*cos (x)/ - 2*cos(x)*sin(x)/*sin(x) \1 + 4*x 1 + 4*x 1 + 4*x / 18*sin (x)*(-1 + 2*x*atan(2*x))*(4*x*cos(x) + sin(x))*atan(2*x)| 12*|- atan (2*x)*\3*\sin (x) - 3*cos (x)/*sin(x) + 2*x*\- 3*cos (x) + 5*sin (x)/*cos(x)/ - ---------------------------------------------------------------- + ------------------------------------------------------------------------ - ---------------------------------------------------------------|*sin(x) | 2 2 2 | | 1 + 4*x / 2\ / 2\ | \ \1 + 4*x / \1 + 4*x / /
$$12 \left(\frac{12 x \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \sin^{3}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \left(2 x \left(5 \sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)} + 3 \left(\sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}\right) \operatorname{atan}^{3}{\left(2 x \right)} - \frac{18 \left(x \left(\sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{18 \left(4 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin{\left(x \right)}$$
Gráfico