Sr Examen

Otras calculadoras

y=3^(arcsin^(2)x)
Derivada de la función/ arcsin/ sin^(2)x/ y=3^(arcsin^(2)x)

Derivada de y=3^(arcsin^(2)x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     2   
 asin (x)
3
3asin⁡2(x)3^{\operatorname{asin}^{2}{\left(x \right)}} 
3^(asin(x)^2)
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       2                  
   asin (x)               
2*3        *asin(x)*log(3)
--------------------------
          ________        
         /      2         
       \/  1 - x
2⋅3asin⁡2(x)log⁡(3)asin⁡(x)1−x2\frac{2 \cdot 3^{\operatorname{asin}^{2}{\left(x \right)}} \log{\left(3 \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}
Simplificar
Segunda derivada [src] 
       2    /                                2          \       
   asin (x) |     1       x*asin(x)    2*asin (x)*log(3)|       
2*3        *|- ------- + ----------- - -----------------|*log(3)
            |        2           3/2              2     |       
            |  -1 + x    /     2\           -1 + x      |       
            \            \1 - x /                       /
2⋅3asin⁡2(x)(xasin⁡(x)(1−x2)32−2log⁡(3)asin⁡2(x)x2−1−1x2−1)log⁡(3)2 \cdot 3^{\operatorname{asin}^{2}{\left(x \right)}} \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \log{\left(3 \right)} \operatorname{asin}^{2}{\left(x \right)}}{x^{2} - 1} - \frac{1}{x^{2} - 1}\right) \log{\left(3 \right)}
Simplificar
Tercera derivada [src] 
       2    /                              2                 3       2                                 2          \       
   asin (x) |  asin(x)        3*x       3*x *asin(x)   4*asin (x)*log (3)   6*asin(x)*log(3)   6*x*asin (x)*log(3)|       
2*3        *|----------- + ---------- + ------------ + ------------------ + ---------------- + -------------------|*log(3)
            |        3/2            2           5/2               3/2                 3/2                    2    |       
            |/     2\      /      2\    /     2\          /     2\            /     2\              /      2\     |       
            \\1 - x /      \-1 + x /    \1 - x /          \1 - x /            \1 - x /              \-1 + x /     /
2⋅3asin⁡2(x)(3x2asin⁡(x)(1−x2)52+6xlog⁡(3)asin⁡2(x)(x2−1)2+3x(x2−1)2+4log⁡(3)2asin⁡3(x)(1−x2)32+asin⁡(x)(1−x2)32+6log⁡(3)asin⁡(x)(1−x2)32)log⁡(3)2 \cdot 3^{\operatorname{asin}^{2}{\left(x \right)}} \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x \log{\left(3 \right)} \operatorname{asin}^{2}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{4 \log{\left(3 \right)}^{2} \operatorname{asin}^{3}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6 \log{\left(3 \right)} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(3 \right)}
Simplificar
Gráfico
Derivada de y=3^(arcsin^(2)x)
    © Sr Examen – Калькулятор