Question

ρ=ΘsinΘ+1\2cosΘ，求dρ/dθ,θ=π/4

求知道的同学给个详解 谢谢啦。

Answer 1

ρ=ΘsinΘ+(1/2)cosΘ
dρ/dΘ=ΘcosΘ+sinΘ-(1/2)sinΘ
=ΘcosΘ+(1/2)sinΘ
dρ/dθ|θ=π/4

=(π/4)cos(π/4)+(1/2)sin(π/4)
=(√2/8)(π+2)

Answer 2

dρ/dθ=sinΘ+ΘcosΘ+1/2[(1/cosΘ)^2 ]*sinΘ
θ=π/4
dρ/dθ=1/2(根号2)*（2+π/4）