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^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- y=(arccos(tres x- dos))^sin5x^(3)
- y es igual a (arc coseno de (3x menos 2)) en el grado seno de 5x en el grado (3)
- y es igual a (arc coseno de (tres x menos dos)) en el grado seno de 5x en el grado (3)
- y=(arccos(3x-2))sin5x(3)
- y=arccos3x-2sin5x3
- y=arccos3x-2^sin5x^3
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Expresiones semejantes
- y=(arccos(3x+2))^sin5x^(3)
Derivada de y=(arccos(3x-2))^sin5x^(3)
Solución
Ha introducido
[src]
3
sin (5*x)
(acos(3*x - 2))
$$\operatorname{acos}^{\sin^{3}{\left(5 x \right)}}{\left(3 x - 2 \right)}$$
acos(3*x - 2)^(sin(5*x)^3)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
3 / 3 \
sin (5*x) | 3*sin (5*x) 2 |
(acos(3*x - 2)) *|- --------------------------------- + 15*sin (5*x)*cos(5*x)*log(acos(3*x - 2))|
| ________________ |
| / 2 |
\ \/ 1 - (3*x - 2) *acos(3*x - 2) /
$$\left(15 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)} - \frac{3 \sin^{3}{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right) \operatorname{acos}^{\sin^{3}{\left(5 x \right)}}{\left(3 x - 2 \right)}$$
Segunda derivada
[src]
3 / 2 2 2 \
sin (5*x) | 2 / sin(5*x) \ 3 2 3*sin (5*x) 30*cos(5*x)*sin(5*x) 3*sin (5*x)*(-2 + 3*x) |
3*(acos(-2 + 3*x)) *|- 25*sin (5*x)*log(acos(-2 + 3*x)) + 3*|5*cos(5*x)*log(acos(-2 + 3*x)) - -----------------------------------| *sin (5*x) + 50*cos (5*x)*log(acos(-2 + 3*x)) + ---------------------------------- - ----------------------------------- - -----------------------------------|*sin(5*x)
| | _________________ | / 2\ 2 _________________ 3/2 |
| | / 2 | \-1 + (-2 + 3*x) /*acos (-2 + 3*x) / 2 / 2\ |
\ \ \/ 1 - (-2 + 3*x) *acos(-2 + 3*x)/ \/ 1 - (-2 + 3*x) *acos(-2 + 3*x) \1 - (-2 + 3*x) / *acos(-2 + 3*x)/
$$3 \left(3 \left(5 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \cos{\left(5 x \right)} - \frac{\sin{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right)^{2} \sin^{3}{\left(5 x \right)} - 25 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \sin^{2}{\left(5 x \right)} + 50 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \cos^{2}{\left(5 x \right)} + \frac{3 \sin^{2}{\left(5 x \right)}}{\left(\left(3 x - 2\right)^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x - 2 \right)}} - \frac{30 \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}} - \frac{3 \left(3 x - 2\right) \sin^{2}{\left(5 x \right)}}{\left(1 - \left(3 x - 2\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right) \sin{\left(5 x \right)} \operatorname{acos}^{\sin^{3}{\left(5 x \right)}}{\left(3 x - 2 \right)}$$
Tercera derivada
[src]
3 / 3 3 3 / 2 2 \ 3 2 2 3 3 2 2 \
sin (5*x) | / sin(5*x) \ 6 3 2 18*sin (5*x) 9*sin (5*x) 3 / sin(5*x) \ | 2 2 3*sin (5*x) 3*sin (5*x)*(-2 + 3*x) 30*cos(5*x)*sin(5*x) | 225*sin (5*x) 450*cos (5*x)*sin(5*x) 27*(-2 + 3*x) *sin (5*x) 27*sin (5*x)*(-2 + 3*x) 135*sin (5*x)*cos(5*x) 135*sin (5*x)*(-2 + 3*x)*cos(5*x) |
3*(acos(-2 + 3*x)) *|9*|5*cos(5*x)*log(acos(-2 + 3*x)) - -----------------------------------| *sin (5*x) + 250*cos (5*x)*log(acos(-2 + 3*x)) - 875*sin (5*x)*cos(5*x)*log(acos(-2 + 3*x)) - ------------------------------------ - ----------------------------------- - 9*sin (5*x)*|5*cos(5*x)*log(acos(-2 + 3*x)) - -----------------------------------|*|- 50*cos (5*x)*log(acos(-2 + 3*x)) + 25*sin (5*x)*log(acos(-2 + 3*x)) - ---------------------------------- + ----------------------------------- + -----------------------------------| + ----------------------------------- - ----------------------------------- - ----------------------------------- - ----------------------------------- + ---------------------------------- - -----------------------------------|
| | _________________ | 3/2 3/2 | _________________ | | / 2\ 2 3/2 _________________ | _________________ _________________ 5/2 2 / 2\ 2 3/2 |
| | / 2 | / 2\ 3 / 2\ | / 2 | | \-1 + (-2 + 3*x) /*acos (-2 + 3*x) / 2\ / 2 | / 2 / 2 / 2\ / 2\ 2 \-1 + (-2 + 3*x) /*acos (-2 + 3*x) / 2\ |
\ \ \/ 1 - (-2 + 3*x) *acos(-2 + 3*x)/ \1 - (-2 + 3*x) / *acos (-2 + 3*x) \1 - (-2 + 3*x) / *acos(-2 + 3*x) \ \/ 1 - (-2 + 3*x) *acos(-2 + 3*x)/ \ \1 - (-2 + 3*x) / *acos(-2 + 3*x) \/ 1 - (-2 + 3*x) *acos(-2 + 3*x)/ \/ 1 - (-2 + 3*x) *acos(-2 + 3*x) \/ 1 - (-2 + 3*x) *acos(-2 + 3*x) \1 - (-2 + 3*x) / *acos(-2 + 3*x) \-1 + (-2 + 3*x) / *acos (-2 + 3*x) \1 - (-2 + 3*x) / *acos(-2 + 3*x)/
$$3 \left(- \frac{27 \left(3 x - 2\right) \sin^{3}{\left(5 x \right)}}{\left(\left(3 x - 2\right)^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(3 x - 2 \right)}} + 9 \left(5 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \cos{\left(5 x \right)} - \frac{\sin{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right)^{3} \sin^{6}{\left(5 x \right)} - 9 \left(5 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \cos{\left(5 x \right)} - \frac{\sin{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right) \left(25 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \sin^{2}{\left(5 x \right)} - 50 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \cos^{2}{\left(5 x \right)} - \frac{3 \sin^{2}{\left(5 x \right)}}{\left(\left(3 x - 2\right)^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x - 2 \right)}} + \frac{30 \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}} + \frac{3 \left(3 x - 2\right) \sin^{2}{\left(5 x \right)}}{\left(1 - \left(3 x - 2\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right) \sin^{3}{\left(5 x \right)} - 875 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)} + 250 \log{\left(\operatorname{acos}{\left(3 x - 2 \right)} \right)} \cos^{3}{\left(5 x \right)} + \frac{135 \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)}}{\left(\left(3 x - 2\right)^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x - 2 \right)}} + \frac{225 \sin^{3}{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}} - \frac{450 \sin{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{\sqrt{1 - \left(3 x - 2\right)^{2}} \operatorname{acos}{\left(3 x - 2 \right)}} - \frac{135 \left(3 x - 2\right) \sin^{2}{\left(5 x \right)} \cos{\left(5 x \right)}}{\left(1 - \left(3 x - 2\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x - 2 \right)}} - \frac{9 \sin^{3}{\left(5 x \right)}}{\left(1 - \left(3 x - 2\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x - 2 \right)}} - \frac{18 \sin^{3}{\left(5 x \right)}}{\left(1 - \left(3 x - 2\right)^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(3 x - 2 \right)}} - \frac{27 \left(3 x - 2\right)^{2} \sin^{3}{\left(5 x \right)}}{\left(1 - \left(3 x - 2\right)^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(3 x - 2 \right)}}\right) \operatorname{acos}^{\sin^{3}{\left(5 x \right)}}{\left(3 x - 2 \right)}$$
Gráfico