## Derivative of Sum of Monomials
General Explanation
In this lesson we will learn how to differentiate a sum of monomials,
such as u(x) + v(x). First, let's derive the rule. We'll begin with the definition of a derivative:
dy f(x+Δx) - f(x) Now, let f(x) = u(x) + v(x). Then, f(x+Δx) = u(x+Δx) + v(x+Δx).
dy u(x+Δx)+v(x+Δx) - [u(x)+v(x)] Now let's distribute the minus sign and switch the positions of the second and third terms.
dy u(x+Δx)-u(x) + v(x+Δx)-v(x) We can see that this is actually the sum of du(x)/dx and dv(x)/dx. As a general rule:
d(u(x)+v(x)) d(u(x)) d((v)x))
Sample Problem
Find:
d(6x
Solution
We will use the general rule for the derivative of the sum of monomials.
d(6x |