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Derivada de la función/ tgx^2/ arctg/ y=sqrtarctgx^2*cos^72x

Derivada de y=sqrtarctgx^2*cos^72x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
      2       49     
t*acot (x)*cos  (2*x)
tacot⁡2(x)cos⁡49(2x)t \operatorname{acot}^{2}{\left(x \right)} \cos^{49}{\left(2 x \right)} 
(t*acot(x)^2)*cos(2*x)^49
Primera derivada [src] 
                                             49             
           2       48                 2*t*cos  (2*x)*acot(x)
- 98*t*acot (x)*cos  (2*x)*sin(2*x) - ----------------------
                                                   2        
                                              1 + x
−98tsin⁡(2x)cos⁡48(2x)acot⁡2(x)−2tcos⁡49(2x)acot⁡(x)x2+1- 98 t \sin{\left(2 x \right)} \cos^{48}{\left(2 x \right)} \operatorname{acot}^{2}{\left(x \right)} - \frac{2 t \cos^{49}{\left(2 x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
               /                                              2                                                       \
       47      |       2    /     2              2     \   cos (2*x)*(1 + 2*x*acot(x))   196*acot(x)*cos(2*x)*sin(2*x)|
2*t*cos  (2*x)*|98*acot (x)*\- cos (2*x) + 48*sin (2*x)/ + --------------------------- + -----------------------------|
               |                                                            2                             2           |
               |                                                    /     2\                         1 + x            |
               \                                                    \1 + x /                                          /
2t(98(48sin⁡2(2x)−cos⁡2(2x))acot⁡2(x)+196sin⁡(2x)cos⁡(2x)acot⁡(x)x2+1+(2xacot⁡(x)+1)cos⁡2(2x)(x2+1)2)cos⁡47(2x)2 t \left(98 \left(48 \sin^{2}{\left(2 x \right)} - \cos^{2}{\left(2 x \right)}\right) \operatorname{acot}^{2}{\left(x \right)} + \frac{196 \sin{\left(2 x \right)} \cos{\left(2 x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{\left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \cos^{2}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cos^{47}{\left(2 x \right)}
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Tercera derivada [src] 
                /          /                       2        \                                                                                                                                                         \
                |   3      |            3*x     4*x *acot(x)|                                                                                                                                                         |
                |cos (2*x)*|-acot(x) + ------ + ------------|                                                                                                                                                         |
                |          |                2           2   |                                                                    2                                       /     2              2     \                 |
        46      |          \           1 + x       1 + x    /          2    /         2                2     \            147*cos (2*x)*(1 + 2*x*acot(x))*sin(2*x)   294*\- cos (2*x) + 48*sin (2*x)/*acot(x)*cos(2*x)|
-4*t*cos  (2*x)*|-------------------------------------------- + 98*acot (x)*\- 145*cos (2*x) + 2256*sin (2*x)/*sin(2*x) + ---------------------------------------- + -------------------------------------------------|
                |                         2                                                                                                      2                                              2                     |
                |                 /     2\                                                                                               /     2\                                          1 + x                      |
                \                 \1 + x /                                                                                               \1 + x /                                                                     /
−4t(98(2256sin⁡2(2x)−145cos⁡2(2x))sin⁡(2x)acot⁡2(x)+294(48sin⁡2(2x)−cos⁡2(2x))cos⁡(2x)acot⁡(x)x2+1+147(2xacot⁡(x)+1)sin⁡(2x)cos⁡2(2x)(x2+1)2+(4x2acot⁡(x)x2+1+3xx2+1−acot⁡(x))cos⁡3(2x)(x2+1)2)cos⁡46(2x)- 4 t \left(98 \left(2256 \sin^{2}{\left(2 x \right)} - 145 \cos^{2}{\left(2 x \right)}\right) \sin{\left(2 x \right)} \operatorname{acot}^{2}{\left(x \right)} + \frac{294 \left(48 \sin^{2}{\left(2 x \right)} - \cos^{2}{\left(2 x \right)}\right) \cos{\left(2 x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{147 \left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \sin{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) \cos^{3}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cos^{46}{\left(2 x \right)}
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