ρ=e^θ                     ( e^(π/2) , π/2 )

dρ/dθ = e^θ

dρ/dθ|(θ =π/2)  = e^(π/2)

x=ρ.cosθ

dx/dθ = -ρ.sinθ + cosθ . (dρ/dθ)

dx/dθ|(θ =π/2) = -e^(π/2) 

y=ρ.sinθ

dy/dθ = ρ.cosθ + sinθ . dρ/dθ

dy/dθ |(θ =π/2)  =  e^(π/2)

dy/dx |θ =π/2

=(dy/dθ |θ =π/2 ) /(dx/dθ|θ =π/2)

= e^(π/2)/[-e^(π/2) ]

=-1