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y=arcsin^3sinx
Derivada de la función/ 3sinx/ sin^3/ arcsin/ y=arcsin^3sinx

Derivada de y=arcsin^3sinx

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Ha introducido [src] 
    3          
asin (x)*sin(x)
sin⁡(x)asin⁡3(x)\sin{\left(x \right)} \operatorname{asin}^{3}{\left(x \right)} 
asin(x)^3*sin(x)
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
                        2          
    3             3*asin (x)*sin(x)
asin (x)*cos(x) + -----------------
                        ________   
                       /      2    
                     \/  1 - x
cos⁡(x)asin⁡3(x)+3sin⁡(x)asin⁡2(x)1−x2\cos{\left(x \right)} \operatorname{asin}^{3}{\left(x \right)} + \frac{3 \sin{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
/      2               /     2       x*asin(x) \          6*asin(x)*cos(x)\        
|- asin (x)*sin(x) + 3*|- ------- + -----------|*sin(x) + ----------------|*asin(x)
|                      |        2           3/2|               ________   |        
|                      |  -1 + x    /     2\   |              /      2    |        
\                      \            \1 - x /   /            \/  1 - x     /
(3(xasin⁡(x)(1−x2)32−2x2−1)sin⁡(x)−sin⁡(x)asin⁡2(x)+6cos⁡(x)asin⁡(x)1−x2)asin⁡(x)\left(3 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{x^{2} - 1}\right) \sin{\left(x \right)} - \sin{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} + \frac{6 \cos{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \operatorname{asin}{\left(x \right)}
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Tercera derivada [src] 
                      /                    2          2     2                 \                2                                                       
      3               |     2          asin (x)    3*x *asin (x)   6*x*asin(x)|          9*asin (x)*sin(x)     /     2       x*asin(x) \               
- asin (x)*cos(x) + 3*|----------- + ----------- + ------------- + -----------|*sin(x) - ----------------- + 9*|- ------- + -----------|*asin(x)*cos(x)
                      |        3/2           3/2            5/2              2|                ________        |        2           3/2|               
                      |/     2\      /     2\       /     2\        /      2\ |               /      2         |  -1 + x    /     2\   |               
                      \\1 - x /      \1 - x /       \1 - x /        \-1 + x / /             \/  1 - x          \            \1 - x /   /
9(xasin⁡(x)(1−x2)32−2x2−1)cos⁡(x)asin⁡(x)+3(3x2asin⁡2(x)(1−x2)52+6xasin⁡(x)(x2−1)2+asin⁡2(x)(1−x2)32+2(1−x2)32)sin⁡(x)−cos⁡(x)asin⁡3(x)−9sin⁡(x)asin⁡2(x)1−x29 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{x^{2} - 1}\right) \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} + 3 \left(\frac{3 x^{2} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \sin{\left(x \right)} - \cos{\left(x \right)} \operatorname{asin}^{3}{\left(x \right)} - \frac{9 \sin{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Gráfico
Derivada de y=arcsin^3sinx
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