The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages. |
Home Differentiation Derivatives of Rational Functions Theorem 2: Sum Rule | |
Search the VIAS Library | Index | |
Theorem 2: Sum Rule
THEOREM 2 (Sum Rule) Suppose u and v depend on the independent variable x. Then for any value of x where du/dx and dv/dx exist, , d(u + v) - du + dv. In other words, the derivative of the sum is the sum of the derivatives. PROOF Let y = u + v, and let Δx ≠ 0 be infinitesimal. Then Taking standard parts, Thus By using the Sum Rule n - 1 times, we see that
|
|
Home Differentiation Derivatives of Rational Functions Theorem 2: Sum Rule |