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
-
¿Cómo usar?
- Derivada de:
-
Derivada de 2*cos(3*x)
-
Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de x^((-2)/7)
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Expresiones idénticas
- y=lnsin^2arcthx^ tres
- y es igual a ln seno de al cuadrado arcthx al cubo
- y es igual a ln seno de al cuadrado arcthx en el grado tres
- y=lnsin2arcthx3
- y=lnsin²arcthx³
- y=lnsin en el grado 2arcthx en el grado 3
Derivada de y=lnsin^2arcthx^3
Solución
Ha introducido
[src]
8 log (sin(atanh(x)))
$$\log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{8}$$
log(sin(atanh(x)))^8
Primera derivada
[src]
7
8*log (sin(atanh(x)))*cos(atanh(x))
-----------------------------------
/ 2\
\1 - x /*sin(atanh(x))
$$\frac{8 \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{7} \cos{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(1 - x^{2}\right) \sin{\left(\operatorname{atanh}{\left(x \right)} \right)}}$$
Segunda derivada
[src]
/ 2 2 \
6 | 7*cos (atanh(x)) cos (atanh(x))*log(sin(atanh(x))) 2*x*cos(atanh(x))*log(sin(atanh(x)))|
8*log (sin(atanh(x)))*|-log(sin(atanh(x))) + ---------------- - --------------------------------- + ------------------------------------|
| 2 2 sin(atanh(x)) |
\ sin (atanh(x)) sin (atanh(x)) /
-----------------------------------------------------------------------------------------------------------------------------------------
2
/ 2\
\-1 + x /
$$\frac{8 \left(\frac{2 x \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)} \cos{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\sin{\left(\operatorname{atanh}{\left(x \right)} \right)}} - \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)} - \frac{\log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\sin^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}} + \frac{7 \cos^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\sin^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}}\right) \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{6}}{\left(x^{2} - 1\right)^{2}}$$
Tercera derivada
[src]
/ 3 2 2 3 2 2 3 2 2 2 2 2 \
5 | 42*cos (atanh(x)) 2*log (sin(atanh(x)))*cos(atanh(x)) 6*x*log (sin(atanh(x))) 2*cos (atanh(x))*log (sin(atanh(x))) 2*log (sin(atanh(x)))*cos(atanh(x)) 21*cos (atanh(x))*log(sin(atanh(x))) 21*cos(atanh(x))*log(sin(atanh(x))) 42*x*cos (atanh(x))*log(sin(atanh(x))) 8*x *log (sin(atanh(x)))*cos(atanh(x)) 6*x*cos (atanh(x))*log (sin(atanh(x)))|
8*log (sin(atanh(x)))*|- ------------------------ + ----------------------------------- + ----------------------- - ------------------------------------ - ----------------------------------- + ------------------------------------ + ----------------------------------- - -------------------------------------- - -------------------------------------- + --------------------------------------|
| / 2\ 3 sin(atanh(x)) 2 / 2\ 3 / 2\ / 2\ 3 / 2\ / 2\ 2 / 2\ / 2\ 2 |
\ \-1 + x /*sin (atanh(x)) -1 + x \-1 + x /*sin (atanh(x)) \-1 + x /*sin(atanh(x)) \-1 + x /*sin (atanh(x)) \-1 + x /*sin(atanh(x)) \-1 + x /*sin (atanh(x)) \-1 + x /*sin(atanh(x)) \-1 + x /*sin (atanh(x)) /
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2
/ 2\
\-1 + x /
$$\frac{8 \left(- \frac{8 x^{2} \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{2} \cos{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin{\left(\operatorname{atanh}{\left(x \right)} \right)}} + \frac{6 x \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{2}}{x^{2} - 1} + \frac{6 x \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{2} \cos^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}} - \frac{42 x \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)} \cos^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin^{2}{\left(\operatorname{atanh}{\left(x \right)} \right)}} + \frac{2 \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{2} \cos{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\sin{\left(\operatorname{atanh}{\left(x \right)} \right)}} - \frac{2 \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{2} \cos{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin{\left(\operatorname{atanh}{\left(x \right)} \right)}} - \frac{2 \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{2} \cos^{3}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin^{3}{\left(\operatorname{atanh}{\left(x \right)} \right)}} + \frac{21 \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)} \cos{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin{\left(\operatorname{atanh}{\left(x \right)} \right)}} + \frac{21 \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)} \cos^{3}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin^{3}{\left(\operatorname{atanh}{\left(x \right)} \right)}} - \frac{42 \cos^{3}{\left(\operatorname{atanh}{\left(x \right)} \right)}}{\left(x^{2} - 1\right) \sin^{3}{\left(\operatorname{atanh}{\left(x \right)} \right)}}\right) \log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{5}}{\left(x^{2} - 1\right)^{2}}$$
Gráfico