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 2*cos(3*x)
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de x^((-2)/7)
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Expresiones idénticas
- y=sin2x3x*arcctg3x^ cinco
- y es igual a seno de 2x3x multiplicar por arcctg3x en el grado 5
- y es igual a seno de 2x3x multiplicar por arcctg3x en el grado cinco
- y=sin2x3x*arcctg3x5
- y=sin2x3x*arcctg3x⁵
- y=sin2x3xarcctg3x^5
- y=sin2x3xarcctg3x5
Derivada de y=sin2x3x*arcctg3x^5
Solución
Ha introducido
[src]
5 sin(2*x)*3*x*acot (3*x)
$$x 3 \sin{\left(2 x \right)} \operatorname{acot}^{5}{\left(3 x \right)}$$
((sin(2*x)*3)*x)*acot(3*x)^5
Primera derivada
[src]
4
5 45*x*acot (3*x)*sin(2*x)
acot (3*x)*(sin(2*x)*3 + 6*x*cos(2*x)) - ------------------------
2
1 + 9*x
$$- \frac{45 x \sin{\left(2 x \right)} \operatorname{acot}^{4}{\left(3 x \right)}}{9 x^{2} + 1} + \left(6 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)}\right) \operatorname{acot}^{5}{\left(3 x \right)}$$
Segunda derivada
[src]
3 / 2 15*(2*x*cos(2*x) + sin(2*x))*acot(3*x) 45*x*(2 + 3*x*acot(3*x))*sin(2*x)\
6*acot (3*x)*|- 2*acot (3*x)*(-cos(2*x) + x*sin(2*x)) - -------------------------------------- + ---------------------------------|
| 2 2 |
| 1 + 9*x / 2\ |
\ \1 + 9*x / /
$$6 \left(\frac{45 x \left(3 x \operatorname{acot}{\left(3 x \right)} + 2\right) \sin{\left(2 x \right)}}{\left(9 x^{2} + 1\right)^{2}} - 2 \left(x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) \operatorname{acot}^{2}{\left(3 x \right)} - \frac{15 \left(2 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) \operatorname{acot}{\left(3 x \right)}}{9 x^{2} + 1}\right) \operatorname{acot}^{3}{\left(3 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| | 2 6 36*x*acot(3*x) 36*x *acot (3*x)| |
| 135*x*|- acot (3*x) + -------- + -------------- + ----------------|*sin(2*x) |
| 2 | 2 2 2 | |
2 | 3 90*acot (3*x)*(-cos(2*x) + x*sin(2*x)) \ 1 + 9*x 1 + 9*x 1 + 9*x / 135*(2 + 3*x*acot(3*x))*(2*x*cos(2*x) + sin(2*x))*acot(3*x)|
6*acot (3*x)*|- 2*acot (3*x)*(3*sin(2*x) + 2*x*cos(2*x)) + -------------------------------------- - ---------------------------------------------------------------------------- + -----------------------------------------------------------|
| 2 2 2 |
| 1 + 9*x / 2\ / 2\ |
\ \1 + 9*x / \1 + 9*x / /
$$6 \left(- \frac{135 x \left(\frac{36 x^{2} \operatorname{acot}^{2}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{36 x \operatorname{acot}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{acot}^{2}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1}\right) \sin{\left(2 x \right)}}{\left(9 x^{2} + 1\right)^{2}} - 2 \left(2 x \cos{\left(2 x \right)} + 3 \sin{\left(2 x \right)}\right) \operatorname{acot}^{3}{\left(3 x \right)} + \frac{90 \left(x \sin{\left(2 x \right)} - \cos{\left(2 x \right)}\right) \operatorname{acot}^{2}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{135 \left(2 x \cos{\left(2 x \right)} + \sin{\left(2 x \right)}\right) \left(3 x \operatorname{acot}{\left(3 x \right)} + 2\right) \operatorname{acot}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2}}\right) \operatorname{acot}^{2}{\left(3 x \right)}$$
Gráfico