We have: #y = frac(e^(x))(x^(2)) - 1#
#Rightarrow y' = frac(d)(dx) (frac(e^(x))(x^(2))) - frac(d)(dx) (1)#
#Rightarrow y' = frac(d)(dx) (frac(e^(x))(x^(2))) - 0#
#Rightarrow y' = frac(d)(dx) (frac(e^(x))(x^(2)))#
#Rightarrow y' = frac(x^(2) cdot frac(d)(dx) (e^(x)) - e^(x) cdot frac(d)(dx) (x^(2)))((x^(2))^(2))#
#Rightarrow y' = frac(x^(2) cdot e^(x) - e^(x) cdot 2 x)(x^(4))#
#Rightarrow y' = frac(e^(x) (x^(2) - 2 x))(x^(4))#
#Rightarrow y' = frac(x e^(x) (x - 2))(x^(4))#
#therefore y' = frac(e^(x) (x - 2))(x^(3))#