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Derivada de la función/ x^2-3/ y=e^t/ y=e^tg^4(x^2-3)

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

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    4/ 2    \
 tan \x  - 3/
E
etan⁡4(x2−3)e^{\tan^{4}{\left(x^{2} - 3 \right)}} 
E^(tan(x^2 - 3)^4)
Primera derivada [src] 
                                        4/ 2    \
       3/ 2    \ /       2/ 2    \\  tan \x  - 3/
8*x*tan \x  - 3/*\1 + tan \x  - 3//*e
8x(tan⁡2(x2−3)+1)etan⁡4(x2−3)tan⁡3(x2−3)8 x \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) e^{\tan^{4}{\left(x^{2} - 3 \right)}} \tan^{3}{\left(x^{2} - 3 \right)}
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Segunda derivada [src] 
                                                                                                                                                4/      2\
     2/      2\ /       2/      2\\ /   2    2/      2\      2 /       2/      2\\      2    4/      2\ /       2/      2\\      /      2\\  tan \-3 + x /
8*tan \-3 + x /*\1 + tan \-3 + x //*\4*x *tan \-3 + x / + 6*x *\1 + tan \-3 + x // + 8*x *tan \-3 + x /*\1 + tan \-3 + x // + tan\-3 + x //*e
8(tan⁡2(x2−3)+1)(8x2(tan⁡2(x2−3)+1)tan⁡4(x2−3)+6x2(tan⁡2(x2−3)+1)+4x2tan⁡2(x2−3)+tan⁡(x2−3))etan⁡4(x2−3)tan⁡2(x2−3)8 \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \left(8 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \tan^{4}{\left(x^{2} - 3 \right)} + 6 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) + 4 x^{2} \tan^{2}{\left(x^{2} - 3 \right)} + \tan{\left(x^{2} - 3 \right)}\right) e^{\tan^{4}{\left(x^{2} - 3 \right)}} \tan^{2}{\left(x^{2} - 3 \right)}
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Tercera derivada [src] 
                         /                                                                                                     2                                                                   2                                                                                                                              2              \     4/      2\             
     /       2/      2\\ |     3/      2\      2    4/      2\     /       2/      2\\    /      2\       2 /       2/      2\\          5/      2\ /       2/      2\\       2 /       2/      2\\     8/      2\       2    2/      2\ /       2/      2\\       2    6/      2\ /       2/      2\\       2 /       2/      2\\     4/      2\|  tan \-3 + x /    /      2\
16*x*\1 + tan \-3 + x //*\6*tan \-3 + x / + 8*x *tan \-3 + x / + 9*\1 + tan \-3 + x //*tan\-3 + x / + 12*x *\1 + tan \-3 + x //  + 12*tan \-3 + x /*\1 + tan \-3 + x // + 32*x *\1 + tan \-3 + x // *tan \-3 + x / + 40*x *tan \-3 + x /*\1 + tan \-3 + x // + 48*x *tan \-3 + x /*\1 + tan \-3 + x // + 72*x *\1 + tan \-3 + x // *tan \-3 + x //*e             *tan\-3 + x /
16x(tan⁡2(x2−3)+1)(32x2(tan⁡2(x2−3)+1)2tan⁡8(x2−3)+72x2(tan⁡2(x2−3)+1)2tan⁡4(x2−3)+12x2(tan⁡2(x2−3)+1)2+48x2(tan⁡2(x2−3)+1)tan⁡6(x2−3)+40x2(tan⁡2(x2−3)+1)tan⁡2(x2−3)+8x2tan⁡4(x2−3)+12(tan⁡2(x2−3)+1)tan⁡5(x2−3)+9(tan⁡2(x2−3)+1)tan⁡(x2−3)+6tan⁡3(x2−3))etan⁡4(x2−3)tan⁡(x2−3)16 x \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \left(32 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right)^{2} \tan^{8}{\left(x^{2} - 3 \right)} + 72 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right)^{2} \tan^{4}{\left(x^{2} - 3 \right)} + 12 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right)^{2} + 48 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \tan^{6}{\left(x^{2} - 3 \right)} + 40 x^{2} \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \tan^{2}{\left(x^{2} - 3 \right)} + 8 x^{2} \tan^{4}{\left(x^{2} - 3 \right)} + 12 \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \tan^{5}{\left(x^{2} - 3 \right)} + 9 \left(\tan^{2}{\left(x^{2} - 3 \right)} + 1\right) \tan{\left(x^{2} - 3 \right)} + 6 \tan^{3}{\left(x^{2} - 3 \right)}\right) e^{\tan^{4}{\left(x^{2} - 3 \right)}} \tan{\left(x^{2} - 3 \right)}
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