Here are the formulas you should remember about derivation:

• Writing f(x) is the same as y. This means that we can write a function as f(x) = 2x + 1 but we can also write it as y = 2x + 1
• Writing f'(x) is the same as dy/dx, and is the same as writing D_x 

Consider c a constant real number and a function defined as

f(x) = c

f'(x) = 0

Consider c a constant real number and a function defined as

f(x) = cx

f'(x) = c

Consider a function in the form

f(x) = ax + b

f'(x) = a

Consider a function in the form

f(x) = xn 

f'(x) = nxn-1

Consider a function in the form

f(x) = ax2 + bx + c

f'(x) = 2ax + b

Consider c a constant real number and a function defined as cf(x)

Consider two constants c and d and consider two function cf(x) and dg(x). The derivative of 

(cf(x) + dg(x))' = cf'(x) + dg'(x)