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y=tg(arcsin^3(2x^4))
Derivada de la función/ sin^3/ arcsin/ y=tg(arcsin^3(2x^4))

Derivada de y=tg(arcsin^3(2x^4))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   /    3/   4\\
tan\asin \2*x //
tan⁡(asin⁡3(2x4))\tan{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} 
tan(asin(2*x^4)^3)
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
    3     2/   4\ /       2/    3/   4\\\
24*x *asin \2*x /*\1 + tan \asin \2*x ///
-----------------------------------------
                 __________              
                /        8               
              \/  1 - 4*x
24x3(tan⁡2(asin⁡3(2x4))+1)asin⁡2(2x4)1−4x8\frac{24 x^{3} \left(\tan^{2}{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} + 1\right) \operatorname{asin}^{2}{\left(2 x^{4} \right)}}{\sqrt{1 - 4 x^{8}}}
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Segunda derivada [src] 
                              /        4            /   4\       8     /   4\       4     3/   4\    /    3/   4\\\           
    2 /       2/    3/   4\\\ |    16*x       3*asin\2*x /   16*x *asin\2*x /   48*x *asin \2*x /*tan\asin \2*x //|     /   4\
24*x *\1 + tan \asin \2*x ///*|- --------- + ------------- + ---------------- - ----------------------------------|*asin\2*x /
                              |          8      __________              3/2                         8             |           
                              |  -1 + 4*x      /        8     /       8\                    -1 + 4*x              |           
                              \              \/  1 - 4*x      \1 - 4*x /                                          /
24x2(tan⁡2(asin⁡3(2x4))+1)(16x8asin⁡(2x4)(1−4x8)32−48x4tan⁡(asin⁡3(2x4))asin⁡3(2x4)4x8−1−16x44x8−1+3asin⁡(2x4)1−4x8)asin⁡(2x4)24 x^{2} \left(\tan^{2}{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} + 1\right) \left(\frac{16 x^{8} \operatorname{asin}{\left(2 x^{4} \right)}}{\left(1 - 4 x^{8}\right)^{\frac{3}{2}}} - \frac{48 x^{4} \tan{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} \operatorname{asin}^{3}{\left(2 x^{4} \right)}}{4 x^{8} - 1} - \frac{16 x^{4}}{4 x^{8} - 1} + \frac{3 \operatorname{asin}{\left(2 x^{4} \right)}}{\sqrt{1 - 4 x^{8}}}\right) \operatorname{asin}{\left(2 x^{4} \right)}
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Tercera derivada [src] 
                             /      2/   4\           8           4     /   4\        8     2/   4\        12     /   4\        16     2/   4\        4     4/   4\    /    3/   4\\        8     6/   4\ /       2/    3/   4\\\         8     3/   4\    /    3/   4\\         8     6/   4\    2/    3/   4\\         12     4/   4\    /    3/   4\\\
     /       2/    3/   4\\\ |3*asin \2*x /       64*x        72*x *asin\2*x /   104*x *asin \2*x /   384*x  *asin\2*x /   384*x  *asin \2*x /   216*x *asin \2*x /*tan\asin \2*x //   576*x *asin \2*x /*\1 + tan \asin \2*x ///   1152*x *asin \2*x /*tan\asin \2*x //   1152*x *asin \2*x /*tan \asin \2*x //   1152*x  *asin \2*x /*tan\asin \2*x //|
48*x*\1 + tan \asin \2*x ///*|------------- + ------------- - ---------------- + ------------------ + ------------------ + ------------------- - ----------------------------------- + ------------------------------------------ + ------------------------------------ + ------------------------------------- + -------------------------------------|
                             |   __________             3/2              8                   3/2                    2                   5/2                           8                                        3/2                                       3/2                                     3/2                                       2            |
                             |  /        8    /       8\         -1 + 4*x          /       8\            /        8\          /       8\                      -1 + 4*x                               /       8\                                /       8\                              /       8\                               /        8\             |
                             \\/  1 - 4*x     \1 - 4*x /                           \1 - 4*x /            \-1 + 4*x /          \1 - 4*x /                                                             \1 - 4*x /                                \1 - 4*x /                              \1 - 4*x /                               \-1 + 4*x /             /
48x(tan⁡2(asin⁡3(2x4))+1)(384x16asin⁡2(2x4)(1−4x8)52+1152x12tan⁡(asin⁡3(2x4))asin⁡4(2x4)(4x8−1)2+384x12asin⁡(2x4)(4x8−1)2+576x8(tan⁡2(asin⁡3(2x4))+1)asin⁡6(2x4)(1−4x8)32+1152x8tan⁡2(asin⁡3(2x4))asin⁡6(2x4)(1−4x8)32+1152x8tan⁡(asin⁡3(2x4))asin⁡3(2x4)(1−4x8)32+104x8asin⁡2(2x4)(1−4x8)32+64x8(1−4x8)32−216x4tan⁡(asin⁡3(2x4))asin⁡4(2x4)4x8−1−72x4asin⁡(2x4)4x8−1+3asin⁡2(2x4)1−4x8)48 x \left(\tan^{2}{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} + 1\right) \left(\frac{384 x^{16} \operatorname{asin}^{2}{\left(2 x^{4} \right)}}{\left(1 - 4 x^{8}\right)^{\frac{5}{2}}} + \frac{1152 x^{12} \tan{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} \operatorname{asin}^{4}{\left(2 x^{4} \right)}}{\left(4 x^{8} - 1\right)^{2}} + \frac{384 x^{12} \operatorname{asin}{\left(2 x^{4} \right)}}{\left(4 x^{8} - 1\right)^{2}} + \frac{576 x^{8} \left(\tan^{2}{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} + 1\right) \operatorname{asin}^{6}{\left(2 x^{4} \right)}}{\left(1 - 4 x^{8}\right)^{\frac{3}{2}}} + \frac{1152 x^{8} \tan^{2}{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} \operatorname{asin}^{6}{\left(2 x^{4} \right)}}{\left(1 - 4 x^{8}\right)^{\frac{3}{2}}} + \frac{1152 x^{8} \tan{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} \operatorname{asin}^{3}{\left(2 x^{4} \right)}}{\left(1 - 4 x^{8}\right)^{\frac{3}{2}}} + \frac{104 x^{8} \operatorname{asin}^{2}{\left(2 x^{4} \right)}}{\left(1 - 4 x^{8}\right)^{\frac{3}{2}}} + \frac{64 x^{8}}{\left(1 - 4 x^{8}\right)^{\frac{3}{2}}} - \frac{216 x^{4} \tan{\left(\operatorname{asin}^{3}{\left(2 x^{4} \right)} \right)} \operatorname{asin}^{4}{\left(2 x^{4} \right)}}{4 x^{8} - 1} - \frac{72 x^{4} \operatorname{asin}{\left(2 x^{4} \right)}}{4 x^{8} - 1} + \frac{3 \operatorname{asin}^{2}{\left(2 x^{4} \right)}}{\sqrt{1 - 4 x^{8}}}\right)
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Gráfico
Derivada de y=tg(arcsin^3(2x^4))
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