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 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=arcsin(sin^4x-cos^4x)
- y es igual a arc seno de ( seno de en el grado 4x menos coseno de en el grado 4x)
- y=arcsin(sin4x-cos4x)
- y=arcsinsin4x-cos4x
- y=arcsin(sin⁴x-cos⁴x)
- y=arcsinsin^4x-cos^4x
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Expresiones semejantes
- y=arcsin(sin^4x+cos^4x)
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Expresiones con funciones
- arcsin
- arcsin(lnx)
- arcsin1/x
- arcsin(4x+1)
- arcsin(x)^sqrt(1-x^2)
- arcsin2^x
- Seno sin
- sin(x)cos(x)
- sin(t)*cos(t)
- sin(3*x^2)/((3*x^2))
- sin(3*x-pi/12)
- sin(5*x+2)
- Coseno cos
- cos(3/x)
- cos(x)^sin(x)
- cos*(x^2)
- cos(x)/(e^x)
- cos(x+3)
Derivada de y=arcsin(sin^4x-cos^4x)
Solución
Ha introducido
[src]
/ 4 4 \ asin\sin (x) - cos (x)/
$$\operatorname{asin}{\left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)} \right)}$$
asin(sin(x)^4 - cos(x)^4)
Primera derivada
[src]
3 3
4*cos (x)*sin(x) + 4*sin (x)*cos(x)
-----------------------------------
__________________________
/ 2
/ / 4 4 \
\/ 1 - \sin (x) - cos (x)/
$$\frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} + 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{\sqrt{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}}$$
Segunda derivada
[src]
/ 2 \
| / 2 2 \ 2 2 |
| 4*\cos (x) + sin (x)/ *cos (x)*sin (x)| / 4 4 \
4*|-1 + --------------------------------------|*\sin (x) - cos (x)/
| 2 |
| / 4 4 \ |
\ 1 - \sin (x) - cos (x)/ /
-------------------------------------------------------------------
__________________________
/ 2
/ / 4 4 \
\/ 1 - \sin (x) - cos (x)/
$$\frac{4 \left(-1 + \frac{4 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}\right) \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)}{\sqrt{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}}$$
Tercera derivada
[src]
/ 2 2 2 2 \
| / 4 4 \ / 2 2 \ 2 2 / 2 2 \ / 4 4 \ 2 2 |
/ 2 2 \ | 3*\sin (x) - cos (x)/ 4*\cos (x) + sin (x)/ *cos (x)*sin (x) 12*\cos (x) + sin (x)/ *\sin (x) - cos (x)/ *cos (x)*sin (x)|
16*\cos (x) + sin (x)/*|-1 - ------------------------ + -------------------------------------- + ------------------------------------------------------------|*cos(x)*sin(x)
| 2 2 2 |
| / 4 4 \ / 4 4 \ / 2\ |
| 1 - \sin (x) - cos (x)/ 1 - \sin (x) - cos (x)/ | / 4 4 \ | |
\ \1 - \sin (x) - cos (x)/ / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
__________________________
/ 2
/ / 4 4 \
\/ 1 - \sin (x) - cos (x)/
$$\frac{16 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \left(-1 + \frac{4 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}} - \frac{3 \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}} + \frac{12 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)^{2} \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}\right)^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)^{2}}}$$
Gráfico