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y=arcctg^5(x^4-3)
Derivada de la función/ x^4-3/ y=arcctg^5(x^4-3)

Derivada de y=arcctg^5(x^4-3)

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

Gráfico:

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Solución

Ha introducido [src] 
    5/ 4    \
acot \x  - 3/
acot⁡5(x4−3)\operatorname{acot}^{5}{\left(x^{4} - 3 \right)} 
acot(x^4 - 3)^5
Gráfica
02468-8-6-4-2-1010-500500
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Primera derivada [src] 
     3     4/ 4    \
-20*x *acot \x  - 3/
--------------------
               2    
       / 4    \     
   1 + \x  - 3/
−20x3acot⁡4(x4−3)(x4−3)2+1- \frac{20 x^{3} \operatorname{acot}^{4}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1}
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Segunda derivada [src] 
                     /                            4           4 /      4\     /      4\\
    2     3/      4\ |        /      4\       16*x         8*x *\-3 + x /*acot\-3 + x /|
20*x *acot \-3 + x /*|- 3*acot\-3 + x / + -------------- + ----------------------------|
                     |                                 2                       2       |
                     |                        /      4\               /      4\        |
                     \                    1 + \-3 + x /           1 + \-3 + x /        /
----------------------------------------------------------------------------------------
                                                  2                                     
                                         /      4\                                      
                                     1 + \-3 + x /
20x2(8x4(x4−3)acot⁡(x4−3)(x4−3)2+1+16x4(x4−3)2+1−3acot⁡(x4−3))acot⁡3(x4−3)(x4−3)2+1\frac{20 x^{2} \left(\frac{8 x^{4} \left(x^{4} - 3\right) \operatorname{acot}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1} + \frac{16 x^{4}}{\left(x^{4} - 3\right)^{2} + 1} - 3 \operatorname{acot}{\left(x^{4} - 3 \right)}\right) \operatorname{acot}^{3}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1}
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Tercera derivada [src] 
                    /                                                                                                                                      2                                                \
                    |                               8             8     2/      4\       4     /      4\        8 /      4\     /      4\       8 /      4\      2/      4\       4     2/      4\ /      4\|
         2/      4\ |        2/      4\         96*x          16*x *acot \-3 + x /   72*x *acot\-3 + x /   192*x *\-3 + x /*acot\-3 + x /   64*x *\-3 + x / *acot \-3 + x /   36*x *acot \-3 + x /*\-3 + x /|
40*x*acot \-3 + x /*|- 3*acot \-3 + x / - ----------------- + -------------------- + ------------------- - ------------------------------ - ------------------------------- + ------------------------------|
                    |                                     2                   2                      2                           2                                 2                               2        |
                    |                     /             2\           /      4\              /      4\            /             2\                  /             2\                       /      4\         |
                    |                     |    /      4\ |       1 + \-3 + x /          1 + \-3 + x /            |    /      4\ |                  |    /      4\ |                   1 + \-3 + x /         |
                    \                     \1 + \-3 + x / /                                                       \1 + \-3 + x / /                  \1 + \-3 + x / /                                         /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                             2                                                                                               
                                                                                                    /      4\                                                                                                
                                                                                                1 + \-3 + x /
40x(−64x8(x4−3)2acot⁡2(x4−3)((x4−3)2+1)2−192x8(x4−3)acot⁡(x4−3)((x4−3)2+1)2+16x8acot⁡2(x4−3)(x4−3)2+1−96x8((x4−3)2+1)2+36x4(x4−3)acot⁡2(x4−3)(x4−3)2+1+72x4acot⁡(x4−3)(x4−3)2+1−3acot⁡2(x4−3))acot⁡2(x4−3)(x4−3)2+1\frac{40 x \left(- \frac{64 x^{8} \left(x^{4} - 3\right)^{2} \operatorname{acot}^{2}{\left(x^{4} - 3 \right)}}{\left(\left(x^{4} - 3\right)^{2} + 1\right)^{2}} - \frac{192 x^{8} \left(x^{4} - 3\right) \operatorname{acot}{\left(x^{4} - 3 \right)}}{\left(\left(x^{4} - 3\right)^{2} + 1\right)^{2}} + \frac{16 x^{8} \operatorname{acot}^{2}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1} - \frac{96 x^{8}}{\left(\left(x^{4} - 3\right)^{2} + 1\right)^{2}} + \frac{36 x^{4} \left(x^{4} - 3\right) \operatorname{acot}^{2}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1} + \frac{72 x^{4} \operatorname{acot}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1} - 3 \operatorname{acot}^{2}{\left(x^{4} - 3 \right)}\right) \operatorname{acot}^{2}{\left(x^{4} - 3 \right)}}{\left(x^{4} - 3\right)^{2} + 1}
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Gráfico
Derivada de y=arcctg^5(x^4-3)
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