Y=e^(2logx+3x)
=e^(logx^2).e^3x
=x^2.e^3x

dy/dx = 2x.e^3x+x^2.3.e^3x
=2x.e^3x+3x^2.e^3x

:)

Hey Sidh,

You want to know the differentiation of

Y = e^(2logx + 3x)

Taking log both sides

Log (y) = loge^ (2logx + 3x)

Log (y) =  (2logx + 3x) log e
Log (y) = 2logx + 3x

Differentiating both sides with respect to x

(1 / y) (dy/dx) = 2 / x + 3

dy/dx = (2/x + 3) y 

dy/dx = (2/x + 3)(2logx +3x)

Hope it helps :)