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:
-
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=arcsin³(cos4x)
- y es igual a arc seno de ³( coseno de 4x)
- y=arcsin³cos4x
Derivada de y=arcsin³(cos4x)
Solución
Ha introducido
[src]
3 asin (cos(4*x))
$$\operatorname{asin}^{3}{\left(\cos{\left(4 x \right)} \right)}$$
asin(cos(4*x))^3
Primera derivada
[src]
2
-12*asin (cos(4*x))*sin(4*x)
----------------------------
_______________
/ 2
\/ 1 - cos (4*x)
$$- \frac{12 \sin{\left(4 x \right)} \operatorname{asin}^{2}{\left(\cos{\left(4 x \right)} \right)}}{\sqrt{1 - \cos^{2}{\left(4 x \right)}}}$$
Segunda derivada
[src]
/ 2 2 \ | 2*sin (4*x) asin(cos(4*x))*cos(4*x) sin (4*x)*asin(cos(4*x))*cos(4*x)| 48*|- -------------- - ----------------------- + ---------------------------------|*asin(cos(4*x)) | 2 _______________ 3/2 | | -1 + cos (4*x) / 2 / 2 \ | \ \/ 1 - cos (4*x) \1 - cos (4*x)/ /
$$48 \left(- \frac{2 \sin^{2}{\left(4 x \right)}}{\cos^{2}{\left(4 x \right)} - 1} - \frac{\cos{\left(4 x \right)} \operatorname{asin}{\left(\cos{\left(4 x \right)} \right)}}{\sqrt{1 - \cos^{2}{\left(4 x \right)}}} + \frac{\sin^{2}{\left(4 x \right)} \cos{\left(4 x \right)} \operatorname{asin}{\left(\cos{\left(4 x \right)} \right)}}{\left(1 - \cos^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}}\right) \operatorname{asin}{\left(\cos{\left(4 x \right)} \right)}$$
Tercera derivada
[src]
/ 2 2 2 2 2 2 2 2 2 2 \
| asin (cos(4*x)) 2*sin (4*x) asin (cos(4*x))*sin (4*x) 6*asin(cos(4*x))*cos(4*x) 3*asin (cos(4*x))*cos (4*x) 6*sin (4*x)*asin(cos(4*x))*cos(4*x) 3*asin (cos(4*x))*cos (4*x)*sin (4*x)|
192*|------------------ - ------------------ - ------------------------- - ------------------------- + --------------------------- - ----------------------------------- - -------------------------------------|*sin(4*x)
| _______________ 3/2 3/2 2 3/2 2 5/2 |
| / 2 / 2 \ / 2 \ -1 + cos (4*x) / 2 \ / 2 \ / 2 \ |
\\/ 1 - cos (4*x) \1 - cos (4*x)/ \1 - cos (4*x)/ \1 - cos (4*x)/ \-1 + cos (4*x)/ \1 - cos (4*x)/ /
$$192 \left(- \frac{6 \cos{\left(4 x \right)} \operatorname{asin}{\left(\cos{\left(4 x \right)} \right)}}{\cos^{2}{\left(4 x \right)} - 1} - \frac{6 \sin^{2}{\left(4 x \right)} \cos{\left(4 x \right)} \operatorname{asin}{\left(\cos{\left(4 x \right)} \right)}}{\left(\cos^{2}{\left(4 x \right)} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(\cos{\left(4 x \right)} \right)}}{\sqrt{1 - \cos^{2}{\left(4 x \right)}}} - \frac{\sin^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(\cos{\left(4 x \right)} \right)}}{\left(1 - \cos^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} - \frac{2 \sin^{2}{\left(4 x \right)}}{\left(1 - \cos^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} + \frac{3 \cos^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(\cos{\left(4 x \right)} \right)}}{\left(1 - \cos^{2}{\left(4 x \right)}\right)^{\frac{3}{2}}} - \frac{3 \sin^{2}{\left(4 x \right)} \cos^{2}{\left(4 x \right)} \operatorname{asin}^{2}{\left(\cos{\left(4 x \right)} \right)}}{\left(1 - \cos^{2}{\left(4 x \right)}\right)^{\frac{5}{2}}}\right) \sin{\left(4 x \right)}$$
Gráfico