# Derivatives

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 Dx

Considering c a constant real number and a function defined as f(x) = c

`f'(x) = 0`

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

`cf'(x) = c(dy/dx)`

Considering two constants c and d and considering two function cf(x) and dg(x). The derivative of

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

Considering c a constant real number and a function defined as f(x) = cx

`f'(x) = c`

Considering a function in the form f(x) = ax + b

`f'(x) = a.`

Considering a function in the form f(x) = xn

`f'(x) = nxn-1`

Considering a function in the form f(x) = ax2 + bx + c

`f'(x) = 2ax + b`

Considering u a function, considering that du/dx is its derivative, and considering u elevated to the power of n as in un

`f'(u) = nun-1du/dx`

Considering u a function considering that du/dx is the derivative of that function, consider f(u)

`f'(u) = (u')du/dx`

Considering the product of two functions uv

`(uv)' = u'v + uv'`