jueves, 12 de septiembre de 2019

derivada imperial

d_{x}^{(1/m)}[x^{n}] = n^{(1/m)}·x^{( (n+(-1))/m )}
d_{x}^{(1/m)}[e^{x}] = e^{(1/m)x}


d_{t}^{(1/m)}[ d_{t}^{(1/m)}[x(t)]^{m} ] + ( a^{(2/m)}( x(t) )^{(1/m)} ) = 0 <==> x(t)=e^{at·i}


d_{x}^{(1/m)}[ f(x)+g(x) ] =[2/2^{m}]= d_{x}^{(1/m)}[f(x)] + d_{x}^{(1/m)}[g(x)]
d_{x}^{(1/m)}[ af(x) ] = a^{(1/m)}·d_{x}^{(1/m)}[f(x)]


d_{x}^{(1/m)}[ ax^{2}+bx ] =[2/2^{m}]= (2ax)^{(1/m)} + b^{(1/m)}


d_{x}^{(1/m)}[ ax^{3}+bx^{2}+cx ] =[3/3^{m}]= (3a)^{(1/m)}·x^{(2/m)}+(2bx)^{(1/m)}+c^{(1/m)}

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