MATH 1300 Study Guide - Fall 2018, Comprehensive Term Test Notes - Trigonometric Functions, Derivative, Graph Of A Function

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1300
• Professor: Shu Xiao Li

Document Summary

Math 1300 lecture 1 notes derivatives of polynomials and exponential functions. In leibniz notation, we write this rule as follows: derivative of a constant function, power functions, we (cid:374)e(cid:454)t look at the fu(cid:374)ctio(cid:374)s f s(cid:454)d (cid:454)(cid:374), (cid:449)here (cid:374) is a positi(cid:448)e i(cid:374)teger. In fact, we found that: for (cid:374) (cid:1008) (cid:449)e fi(cid:374)d the deri(cid:448)ati(cid:448)e of f s(cid:454)d (cid:454)(cid:1008) as follo(cid:449)s, comparing the equations in (1), (2), and (3), we see a pattern emerging. It seems to be a reasonable guess that, when n is a positive integer, sdydxdsxn d. (cid:374)(cid:454)(cid:374)(cid:1006)(cid:1005): this turns out to be true, the power rule. If n is a positive integer, then: first proof, the formula, can be verified simply by multiplying out the right-hand side (or by summing the second factor as a geometric series). If f s(cid:454)d (cid:454)(cid:374), (cid:449)e can use for f 9sad and the equation above to write: second proof. Math 1300 lecture 2 notes power rule and new derivatives from old.