Question

Qual a derivada de x^x^x

Answer 1

Resposta:

y = x^x^x

ln y = (x^x)* ln x

y = e^[(x^x)* ln x]

g=x^x

ln g =x* ln x

g=e^(x*lnx)

y = e^[e^(x*lnx)* ln x]

y' = [e^(x*lnx)* ln x]' * e^[e^(x*lnx)* ln x]

y' = [(e^(x*lnx))'* ln x + e^(x*lnx) *(ln x)'] * e^[e^(x*lnx)* ln x]

y' = [ (x* lnx)'*e^(x*lnx)* ln x + e^(x*lnx) *1/x] * e^[e^(x*lnx)* ln x]

y' = [ ((x)'* lnx + x* (lnx)')*e^(x*lnx)* ln x + e^(x*lnx) *1/x] * e^[e^(x*lnx)* ln x]

y' = [ (1* lnx + x* 1/x)*e^(x*lnx)* ln x + e^(x*lnx) *1/x] * e^[e^(x*lnx)* ln x]

y' = [ (ln²x + lnx)*e^(x*lnx) + (1/x)* e^(x*lnx)] * x^x^x