Wave-functions help!

Ψ1 = sin(𝑘𝑥)

and

Ψ2 = e^𝑖𝑘𝑥 = 𝑐𝑜𝑠(𝑘𝑥) + 𝑖sin(𝑘𝑥)

(i) Determine the action of the linear momentum operator (𝑝̂𝑥 = 𝑖ℏ 𝑑⁄𝑑𝑥) on each wavefunction.

Not sure how to do this
thank you

apply the operator to each wavefunction, as it says in the question:

𝑝̂ Ψ₁ = 𝑖ℏ 𝑑⁄𝑑𝑥 (sin(𝑘𝑥)) = 𝑖ℏ 𝑑(sin(𝑘𝑥)) ⁄𝑑𝑥
now do the maths (ie differentiate sin(kx) wrt x and you are done with the first one

Thank you very much!

assuming you've managed both, I'd say it's worth making a comment about whether or not each wavefunction corresponds to an eigenstate of the momentum operator.

I assume you're pretty new to quantum mechanics, so if you have any questions about what those things mean then do ask