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y=arctg(sinx^2)
Derivada de la función/ arctg/ sinx^2/ y=arctg(sinx^2)

Derivada de y=arctg(sinx^2)

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

Ha introducido [src] 
    /   2   \
atan\sin (x)/
atan⁡(sin⁡2(x))\operatorname{atan}{\left(\sin^{2}{\left(x \right)} \right)} 
atan(sin(x)^2)
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
2*cos(x)*sin(x)
---------------
         4     
  1 + sin (x)
2sin⁡(x)cos⁡(x)sin⁡4(x)+1\frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\sin^{4}{\left(x \right)} + 1}
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Segunda derivada [src] 
  /                         2       4   \
  |   2         2      4*cos (x)*sin (x)|
2*|cos (x) - sin (x) - -----------------|
  |                              4      |
  \                       1 + sin (x)   /
-----------------------------------------
                      4                  
               1 + sin (x)
2(−sin⁡2(x)+cos⁡2(x)−4sin⁡4(x)cos⁡2(x)sin⁡4(x)+1)sin⁡4(x)+1\frac{2 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} - \frac{4 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{4}{\left(x \right)} + 1}\right)}{\sin^{4}{\left(x \right)} + 1}
Simplificar
Tercera derivada [src] 
  /           4            2       2           2       6   \              
  |      3*sin (x)    5*cos (x)*sin (x)   8*cos (x)*sin (x)|              
8*|-1 + ----------- - ----------------- + -----------------|*cos(x)*sin(x)
  |            4                4                        2 |              
  |     1 + sin (x)      1 + sin (x)        /       4   \  |              
  \                                         \1 + sin (x)/  /              
--------------------------------------------------------------------------
                                      4                                   
                               1 + sin (x)
8(−1+3sin⁡4(x)sin⁡4(x)+1−5sin⁡2(x)cos⁡2(x)sin⁡4(x)+1+8sin⁡6(x)cos⁡2(x)(sin⁡4(x)+1)2)sin⁡(x)cos⁡(x)sin⁡4(x)+1\frac{8 \left(-1 + \frac{3 \sin^{4}{\left(x \right)}}{\sin^{4}{\left(x \right)} + 1} - \frac{5 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{4}{\left(x \right)} + 1} + \frac{8 \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{4}{\left(x \right)} + 1\right)^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\sin^{4}{\left(x \right)} + 1}
Simplificar
Gráfico
Derivada de y=arctg(sinx^2)
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