We find the derivative of each term of f, then add those derivatives together:
The same idea works for differences. The derivative of a difference is the difference of the derivatives: (f – g)' = f ' – g '.
Let f(x) = sin x – cos x. Find f ' (x).
We take the difference of the derivatives of the terms:
The fun comes in when we start combining other rules with the addition/subtraction rule.
Find the derivative of the polynomial f(x) = 5x3 – 4x2.
We find the derivative of each piece, then combine. Notice that we're also using the rule for multiplication-by-a-constant.
Find the derivative of the polynomial
f(x) = 6x7 + 5x4 – 3x2 + 5.
We need to find the derivative of each term, and then combine those derivatives, keeping the addition/subtraction as in the original function. For the sake of organization, find the derivative of each term first: