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y=x^3arcsin√x+1/x^2cosx

Derivada de y=x^3arcsin√x+1/x^2cosx

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

Ha introducido [src]
 3     /  ___\   cos(x)
x *asin\\/ x / + ------
                    2  
                   x   
x3asin(x)+cos(x)x2x^{3} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cos{\left(x \right)}}{x^{2}}
x^3*asin(sqrt(x)) + cos(x)/x^2
Gráfica
02468-8-6-4-2-1010-20002000
Primera derivada [src]
     5/2                                          
    x         sin(x)   2*cos(x)      2     /  ___\
----------- - ------ - -------- + 3*x *asin\\/ x /
    _______      2         3                      
2*\/ 1 - x      x         x                       
x5221x+3x2asin(x)sin(x)x22cos(x)x3\frac{x^{\frac{5}{2}}}{2 \sqrt{1 - x}} + 3 x^{2} \operatorname{asin}{\left(\sqrt{x} \right)} - \frac{\sin{\left(x \right)}}{x^{2}} - \frac{2 \cos{\left(x \right)}}{x^{3}}
Segunda derivada [src]
                                                        5/2             3/2  
  cos(x)   4*sin(x)           /  ___\   6*cos(x)       x            11*x     
- ------ + -------- + 6*x*asin\\/ x / + -------- + ------------ + -----------
     2         3                            4               3/2       _______
    x         x                            x       4*(1 - x)      4*\/ 1 - x 
x524(1x)32+11x3241x+6xasin(x)cos(x)x2+4sin(x)x3+6cos(x)x4\frac{x^{\frac{5}{2}}}{4 \left(1 - x\right)^{\frac{3}{2}}} + \frac{11 x^{\frac{3}{2}}}{4 \sqrt{1 - x}} + 6 x \operatorname{asin}{\left(\sqrt{x} \right)} - \frac{\cos{\left(x \right)}}{x^{2}} + \frac{4 \sin{\left(x \right)}}{x^{3}} + \frac{6 \cos{\left(x \right)}}{x^{4}}
Tercera derivada [src]
                                                      3/2                      5/2             ___ 
      /  ___\   sin(x)   24*cos(x)   18*sin(x)     2*x        6*cos(x)      3*x           57*\/ x  
6*asin\\/ x / + ------ - --------- - --------- + ---------- + -------- + ------------ + -----------
                   2          5           4             3/2       3               5/2       _______
                  x          x           x       (1 - x)         x       8*(1 - x)      8*\/ 1 - x 
3x528(1x)52+2x32(1x)32+57x81x+6asin(x)+sin(x)x2+6cos(x)x318sin(x)x424cos(x)x5\frac{3 x^{\frac{5}{2}}}{8 \left(1 - x\right)^{\frac{5}{2}}} + \frac{2 x^{\frac{3}{2}}}{\left(1 - x\right)^{\frac{3}{2}}} + \frac{57 \sqrt{x}}{8 \sqrt{1 - x}} + 6 \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\sin{\left(x \right)}}{x^{2}} + \frac{6 \cos{\left(x \right)}}{x^{3}} - \frac{18 \sin{\left(x \right)}}{x^{4}} - \frac{24 \cos{\left(x \right)}}{x^{5}}
Gráfico
Derivada de y=x^3arcsin√x+1/x^2cosx