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y=lnsin^2arcthx^3
Derivada de la función/ sin^2/ y=lnsin^2arcthx^3

Derivada de y=lnsin^2arcthx^3

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   8               
log (sin(atanh(x)))
log⁡(sin⁡(atanh⁡(x)))8\log{\left(\sin{\left(\operatorname{atanh}{\left(x \right)} \right)} \right)}^{8} 
log(sin(atanh(x)))^8
Gráfica
02468-8-6-4-2-1010-5000025000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     7                             
8*log (sin(atanh(x)))*cos(atanh(x))
-----------------------------------
       /     2\                    
       \1 - x /*sin(atanh(x))
8log⁡(sin⁡(atanh⁡(x)))7cos⁡(atanh⁡(x))(1−x2)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)}}
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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))                                                /
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                                                                         2                                                               
                                                                /      2\                                                                
                                                                \-1 + x /
8(2xlog⁡(sin⁡(atanh⁡(x)))cos⁡(atanh⁡(x))sin⁡(atanh⁡(x))−log⁡(sin⁡(atanh⁡(x)))−log⁡(sin⁡(atanh⁡(x)))cos⁡2(atanh⁡(x))sin⁡2(atanh⁡(x))+7cos⁡2(atanh⁡(x))sin⁡2(atanh⁡(x)))log⁡(sin⁡(atanh⁡(x)))6(x2−1)2\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}}
Simplificar
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\                                                                                                                                                                                               
                                                                                                                                                                                               \-1 + x /
8(−8x2log⁡(sin⁡(atanh⁡(x)))2cos⁡(atanh⁡(x))(x2−1)sin⁡(atanh⁡(x))+6xlog⁡(sin⁡(atanh⁡(x)))2x2−1+6xlog⁡(sin⁡(atanh⁡(x)))2cos⁡2(atanh⁡(x))(x2−1)sin⁡2(atanh⁡(x))−42xlog⁡(sin⁡(atanh⁡(x)))cos⁡2(atanh⁡(x))(x2−1)sin⁡2(atanh⁡(x))+2log⁡(sin⁡(atanh⁡(x)))2cos⁡(atanh⁡(x))sin⁡(atanh⁡(x))−2log⁡(sin⁡(atanh⁡(x)))2cos⁡(atanh⁡(x))(x2−1)sin⁡(atanh⁡(x))−2log⁡(sin⁡(atanh⁡(x)))2cos⁡3(atanh⁡(x))(x2−1)sin⁡3(atanh⁡(x))+21log⁡(sin⁡(atanh⁡(x)))cos⁡(atanh⁡(x))(x2−1)sin⁡(atanh⁡(x))+21log⁡(sin⁡(atanh⁡(x)))cos⁡3(atanh⁡(x))(x2−1)sin⁡3(atanh⁡(x))−42cos⁡3(atanh⁡(x))(x2−1)sin⁡3(atanh⁡(x)))log⁡(sin⁡(atanh⁡(x)))5(x2−1)2\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}}
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Gráfico
Derivada de y=lnsin^2arcthx^3
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