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^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=arctg(√(uno -cos³x))
- y es igual a arctg(√(1 menos coseno de ³x))
- y es igual a arctg(√(uno menos coseno de ³x))
- y=arctg√1-cos³x
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Expresiones semejantes
- y=arctg(√(1+cos³x))
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Expresiones con funciones
- arctg
- arctg^2(1/x)
Derivada de y=arctg(√(1-cos³x))
Solución
Ha introducido
[src]
/ _____________\
| / 3 |
atan\\/ 1 - cos (x) /
$$\operatorname{atan}{\left(\sqrt{1 - \cos^{3}{\left(x \right)}} \right)}$$
atan(sqrt(1 - cos(x)^3))
Primera derivada
[src]
2
3*cos (x)*sin(x)
--------------------------------
_____________
/ 3 / 3 \
2*\/ 1 - cos (x) *\2 - cos (x)/
$$\frac{3 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{2 \sqrt{1 - \cos^{3}{\left(x \right)}} \left(2 - \cos^{3}{\left(x \right)}\right)}$$
Segunda derivada
[src]
/ 2 3 2 3 2 \
| 2 cos (x) 3*cos (x)*sin (x) 3*cos (x)*sin (x)|
3*|sin (x) - ------- - ----------------- + -----------------|*cos(x)
| 2 / 3 \ / 3 \ |
\ 2*\-2 + cos (x)/ 4*\1 - cos (x)/ /
--------------------------------------------------------------------
_____________
/ 3 / 3 \
\/ 1 - cos (x) *\-2 + cos (x)/
$$\frac{3 \left(\sin^{2}{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{2} - \frac{3 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{2 \left(\cos^{3}{\left(x \right)} - 2\right)} + \frac{3 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{4 \left(1 - \cos^{3}{\left(x \right)}\right)}\right) \cos{\left(x \right)}}{\sqrt{1 - \cos^{3}{\left(x \right)}} \left(\cos^{3}{\left(x \right)} - 2\right)}$$
Tercera derivada
[src]
/ 2 5 5 6 2 3 2 6 2 3 2 6 2 \
| 2 7*cos (x) 9*cos (x) 9*cos (x) 9*cos (x)*sin (x) 9*cos (x)*sin (x) 27*cos (x)*sin (x) 9*cos (x)*sin (x) 9*cos (x)*sin (x) |
3*|- sin (x) + --------- - ---------------- + --------------- - ----------------- + ----------------- - ------------------ - ----------------- + ------------------------------|*sin(x)
| 2 / 3 \ / 3 \ 2 3 2 / 3 \ / 3 \ / 3 \|
| 2*\-2 + cos (x)/ 4*\1 - cos (x)/ / 3 \ -2 + cos (x) / 3 \ 2*\1 - cos (x)/ 2*\1 - cos (x)/*\-2 + cos (x)/|
\ \-2 + cos (x)/ 8*\1 - cos (x)/ /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________
/ 3 / 3 \
\/ 1 - cos (x) *\-2 + cos (x)/
$$\frac{3 \left(- \sin^{2}{\left(x \right)} + \frac{7 \cos^{2}{\left(x \right)}}{2} + \frac{9 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)} - 2} - \frac{9 \cos^{5}{\left(x \right)}}{2 \left(\cos^{3}{\left(x \right)} - 2\right)} - \frac{9 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{\left(\cos^{3}{\left(x \right)} - 2\right)^{2}} - \frac{9 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{2 \left(1 - \cos^{3}{\left(x \right)}\right)} + \frac{9 \cos^{5}{\left(x \right)}}{4 \left(1 - \cos^{3}{\left(x \right)}\right)} + \frac{9 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{2 \left(1 - \cos^{3}{\left(x \right)}\right) \left(\cos^{3}{\left(x \right)} - 2\right)} - \frac{27 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{8 \left(1 - \cos^{3}{\left(x \right)}\right)^{2}}\right) \sin{\left(x \right)}}{\sqrt{1 - \cos^{3}{\left(x \right)}} \left(\cos^{3}{\left(x \right)} - 2\right)}$$
Gráfico