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xln(cos(x))-xln(arcsin(x))
Derivada de la función/ sin(x)/ cos(x)/ arcsin/ xln(cos(x))-xln(arcsin(x))

Derivada de xln(cos(x))-xln(arcsin(x))

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

Ha introducido [src] 
x*log(cos(x)) - x*log(asin(x))
xlog⁡(cos⁡(x))−xlog⁡(asin⁡(x))x \log{\left(\cos{\left(x \right)} \right)} - x \log{\left(\operatorname{asin}{\left(x \right)} \right)} 
x*log(cos(x)) - x*log(asin(x))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                         x            x*sin(x)              
-log(asin(x)) - ------------------- - -------- + log(cos(x))
                   ________            cos(x)               
                  /      2                                  
                \/  1 - x  *asin(x)
−xsin⁡(x)cos⁡(x)−x1−x2asin⁡(x)+log⁡(cos⁡(x))−log⁡(asin⁡(x))- \frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \log{\left(\cos{\left(x \right)} \right)} - \log{\left(\operatorname{asin}{\left(x \right)} \right)}
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Segunda derivada [src] 
 /                                                               2                2        \
 |             2            2*sin(x)           x            x*sin (x)            x         |
-|x + ------------------- + -------- + ------------------ + --------- + -------------------|
 |       ________            cos(x)    /      2\     2          2               3/2        |
 |      /      2                       \-1 + x /*asin (x)    cos (x)    /     2\           |
 \    \/  1 - x  *asin(x)                                               \1 - x /   *asin(x)/
−(x2(1−x2)32asin⁡(x)+xsin⁡2(x)cos⁡2(x)+x+x(x2−1)asin⁡2(x)+2sin⁡(x)cos⁡(x)+21−x2asin⁡(x))- (\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{x \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + x + \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{2}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}})
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Tercera derivada [src] 
                               2                                       3                                                     3                 2       
             3            3*sin (x)           4*x                   3*x                   2*x            2*x*sin(x)   2*x*sin (x)           3*x        
-3 - ------------------ - --------- - ------------------- - ------------------- - -------------------- - ---------- - ----------- + -------------------
     /      2\     2          2               3/2                   5/2                   3/2              cos(x)          3                 2         
     \-1 + x /*asin (x)    cos (x)    /     2\              /     2\              /     2\        3                     cos (x)     /      2\      2   
                                      \1 - x /   *asin(x)   \1 - x /   *asin(x)   \1 - x /   *asin (x)                              \-1 + x / *asin (x)
−3x3(1−x2)52asin⁡(x)+3x2(x2−1)2asin⁡2(x)−2xsin⁡3(x)cos⁡3(x)−2xsin⁡(x)cos⁡(x)−4x(1−x2)32asin⁡(x)−2x(1−x2)32asin⁡3(x)−3sin⁡2(x)cos⁡2(x)−3−3(x2−1)asin⁡2(x)- \frac{3 x^{3}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} + \frac{3 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} - \frac{2 x \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 x \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{4 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} - \frac{2 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} - \frac{3 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3 - \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}}
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Gráfico
Derivada de xln(cos(x))-xln(arcsin(x))
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