MATH 1680 Lecture Notes - Lecture 1: Constant Function, Product Rule, 2 On
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Rule #1 derivative of a constant (cid:1855) is a constant (cid:1856)(cid:1856)(cid:1876)(cid:4666)(cid:1855)(cid:4667)=(cid:882) This is (cid:271)asi(cid:272)all(cid:455) sa(cid:455)i(cid:374)g (cid:862)the deri(cid:448)ati(cid:448)e of(cid:863) (cid:449)ith respe(cid:272)t to (cid:1876). The derivative of a constant function is always zero. Example: (cid:1858)(cid:4666)(cid:1876)(cid:4667)= (cid:885) (cid:1858) (cid:4666)(cid:1876)(cid:4667)=(cid:1856)(cid:1856)(cid:1876)(cid:4666) (cid:885)(cid:4667)=(cid:882) where (cid:1858) read as (cid:862)(cid:1858) pri(cid:373)e(cid:863) (cid:1856)(cid:1856)(cid:1876)(cid:4666)(cid:1876)(cid:4667)=(cid:1866) (cid:1876) (cid:2869) Power rule: replicate whatever the power is as the coefficient, then subtract 1 from the power. Rule #3 derivative of a constant multiply of a function (cid:1856)(cid:1856)(cid:1876)[(cid:1855)(cid:1858)(cid:4666)(cid:1876)(cid:4667)]=(cid:1855)(cid:1856)(cid:1856)(cid:1876)[(cid:1858)(cid:4666)(cid:1876)(cid:4667)] This rule is similar to the power rule. When there is a coefficient multiple whatever the power is to it in addition to subtracting one from coefficient. Example: (cid:1858)(cid:4666)(cid:1876)(cid:4667)= (cid:885) (cid:1876) expand function so it is easier to solve; (cid:2869) is the same as (cid:2869)(cid:3117)/(cid:3118) (cid:885)(cid:883) (cid:883)(cid:1876)(cid:2869)/(cid:2870) (cid:2869)(cid:3117)/(cid:3118) is the same as (cid:1876) (cid:3117)(cid:3118) (cid:885) (cid:1876) (cid:2869)(cid:2870) Because in the original function (cid:1876) was in the denominator, put it back in that form for the.
