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 sin(2*x+3)
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Derivada de (1-2*x)^3
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Derivada de 5/x^4
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Derivada de x^3/x
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Expresiones idénticas
- y=sin^86x×arrctg dos x^2
- y es igual a seno de en el grado 86x×arrctg2x al cuadrado
- y es igual a seno de en el grado 86x×arrctg dos x al cuadrado
- y=sin86x×arrctg2x2
- y=sin⁸6x×arrctg2x²
- y=sin en el grado 86x×arrctg2x en el grado 2
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Expresiones con funciones
- Seno sin
- sin(2*x+3)
- sin^3x
- sin(8*x)
- sin(x)+(3*x)^6
- sin(2*y)
Derivada de y=sin^86x×arrctg2x^2
Solución
Ha introducido
[src]
8 2 sin (6*x)*acot (2*x)
$$\sin^{8}{\left(6 x \right)} \operatorname{acot}^{2}{\left(2 x \right)}$$
sin(6*x)^8*acot(2*x)^2
Primera derivada
[src]
8
4*sin (6*x)*acot(2*x) 2 7
- --------------------- + 48*acot (2*x)*sin (6*x)*cos(6*x)
2
1 + 4*x
$$48 \sin^{7}{\left(6 x \right)} \cos{\left(6 x \right)} \operatorname{acot}^{2}{\left(2 x \right)} - \frac{4 \sin^{8}{\left(6 x \right)} \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada
[src]
/ 2 \
6 | 2 / 2 2 \ sin (6*x)*(1 + 4*x*acot(2*x)) 48*acot(2*x)*cos(6*x)*sin(6*x)|
8*sin (6*x)*|- 36*acot (2*x)*\sin (6*x) - 7*cos (6*x)/ + ----------------------------- - ------------------------------|
| 2 2 |
| / 2\ 1 + 4*x |
\ \1 + 4*x / /
$$8 \left(- 36 \left(\sin^{2}{\left(6 x \right)} - 7 \cos^{2}{\left(6 x \right)}\right) \operatorname{acot}^{2}{\left(2 x \right)} - \frac{48 \sin{\left(6 x \right)} \cos{\left(6 x \right)} \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{\left(4 x \operatorname{acot}{\left(2 x \right)} + 1\right) \sin^{2}{\left(6 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{6}{\left(6 x \right)}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 | 6*x 16*x *acot(2*x)| |
| sin (6*x)*|-acot(2*x) + -------- + ---------------| |
| | 2 2 | 2 / 2 2 \ |
5 | \ 1 + 4*x 1 + 4*x / 2 / 2 2 \ 36*sin (6*x)*(1 + 4*x*acot(2*x))*cos(6*x) 108*\sin (6*x) - 7*cos (6*x)/*acot(2*x)*sin(6*x)|
32*sin (6*x)*|- --------------------------------------------------- - 108*acot (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 / /
$$32 \left(- 108 \left(11 \sin^{2}{\left(6 x \right)} - 21 \cos^{2}{\left(6 x \right)}\right) \cos{\left(6 x \right)} \operatorname{acot}^{2}{\left(2 x \right)} + \frac{108 \left(\sin^{2}{\left(6 x \right)} - 7 \cos^{2}{\left(6 x \right)}\right) \sin{\left(6 x \right)} \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{36 \left(4 x \operatorname{acot}{\left(2 x \right)} + 1\right) \sin^{2}{\left(6 x \right)} \cos{\left(6 x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{\left(\frac{16 x^{2} \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{6 x}{4 x^{2} + 1} - \operatorname{acot}{\left(2 x \right)}\right) \sin^{3}{\left(6 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{5}{\left(6 x \right)}$$
Gráfico