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y=sqrtatansqrtx
Derivada de la función/ sqrtx/ y=sqrtatansqrtx

Derivada de y=sqrtatansqrtx

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   _____________
  /     /  ___\ 
\/  atan\\/ x /
atan⁡(x)\sqrt{\operatorname{atan}{\left(\sqrt{x} \right)}} 
sqrt(atan(sqrt(x)))
Gráfica
02468-8-6-4-2-101002
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Primera derivada [src] 
               1                
--------------------------------
                   _____________
    ___           /     /  ___\ 
4*\/ x *(1 + x)*\/  atan\\/ x /
14x(x+1)atan⁡(x)\frac{1}{4 \sqrt{x} \left(x + 1\right) \sqrt{\operatorname{atan}{\left(\sqrt{x} \right)}}}
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Segunda derivada [src] 
 / 2           4                   1          \ 
-|---- + ------------- + ---------------------| 
 | 3/2     ___                         /  ___\| 
 \x      \/ x *(1 + x)   x*(1 + x)*atan\\/ x // 
------------------------------------------------
                        _____________           
                       /     /  ___\            
          16*(1 + x)*\/  atan\\/ x /
−1x(x+1)atan⁡(x)+4x(x+1)+2x3216(x+1)atan⁡(x)- \frac{\frac{1}{x \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{4}{\sqrt{x} \left(x + 1\right)} + \frac{2}{x^{\frac{3}{2}}}}{16 \left(x + 1\right) \sqrt{\operatorname{atan}{\left(\sqrt{x} \right)}}}
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Tercera derivada [src] 
 12         16              32                     3                          6                        12          
---- + ------------ + -------------- + -------------------------- + ---------------------- + ----------------------
 5/2    3/2             ___        2    3/2        2     2/  ___\    2             /  ___\            2     /  ___\
x      x   *(1 + x)   \/ x *(1 + x)    x   *(1 + x) *atan \\/ x /   x *(1 + x)*atan\\/ x /   x*(1 + x) *atan\\/ x /
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                                                          _____________                                            
                                                         /     /  ___\                                             
                                            64*(1 + x)*\/  atan\\/ x /
12x(x+1)2atan⁡(x)+6x2(x+1)atan⁡(x)+32x(x+1)2+16x32(x+1)+3x32(x+1)2atan⁡2(x)+12x5264(x+1)atan⁡(x)\frac{\frac{12}{x \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{6}{x^{2} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{32}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{16}{x^{\frac{3}{2}} \left(x + 1\right)} + \frac{3}{x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{12}{x^{\frac{5}{2}}}}{64 \left(x + 1\right) \sqrt{\operatorname{atan}{\left(\sqrt{x} \right)}}}
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Gráfico
Derivada de y=sqrtatansqrtx
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