1. Express in your own words the sum and difference rules for differentiation....?

Question

1. Express in your own words the sum and difference rules for differentiation. Use an example to illustrate each rule.

Answer 1

1. The derivative of the sum of two functions is the sum of their derivatives.

d/dx[x^2 + 3x] = d/dx[x^2] + d/dx[3x] = 2x + 3.

2. The derivative of the difference of two functions is the difference of their derivatives.

d/dx[sin(x) - x^3] = d/dx[sin(x)] - d/dx[x^3] = cos(x) - 3x^2.

Answer 2

derivative of the sum (difference) is the sum (diference) of the derivatives