I can't get over this error "undefined local variable or method `f' " Any reason why?

I am trying to get my submit button for to be on a different page but I get this error. I have the following in my show.html.erb,

<%= render 'form' %>

<button type="button" class="btn btn-primary"><%= f.submit %></button>

This is in my _form.html.erb page,

<% form_for @post do |f| %>
      </div>
    <p>
         <%= f.label :body %><br>
         <%= f.text_area :body %>
    </p>
    <p>
        <%= f.submit %>
    </p>
<% end %>

This is in my posts_controller.rb,

class PostsController < ApplicationController
def index
    @posts = Post.all.order("created_at DESC")
end
def welcome
    @user = User.find(session[:user_id])
    @post = Post.find(params[:id])
    @posts = Post.order("created_at desc").limit(4).offset(1)
    @signed_in_user = session[:user_id]
end
def new 
    @post = Post.new
end
def create         
    @post = Post.new(post_params)

    @post.user_id = @signed_in_user

if  @post.save 
    redirect_to dashboard_path 
else
    render 'new'
end
end
def show
    @user = User.find(session[:user_id])
    @post = Post.find(params[:id])
    @posts = Post.order("created_at desc").limit(4).offset(1)
    @signed_in_user = session[:user_id]

end
def edit
    @post = Post.find(params[:id])
end

def update
    @post = Post.find(params[:id])

    if @post.update(params[:post].permit(:body))
        redirect_to @post
    else
        render 'edit'
    end
end
def destroy
    @post = Post.find(params[:id])
    @post.user_id = @signed_in_user

    @post.destroy

    redirect_to posts_path
end

private
def post_params
    params.require(:post).permit(:body)
end
end

I have even tried rendering partials thinking that maybe it could help, I have tried several things overall but can't seem to figure this out. I am sure its very simple and I am missing it but if you know how to fix it then post your answer and thank you in advance! I can also add any other code you may need to see that can help this process!