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Derivatives of Trig. Functions

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    Derivatives of Trig. Functions Derivatives of Trig. Functions Presentation Transcript

    • Derivatives of Trigonometric Functions
    • Here are the Derivatives of Trigonometric Functions: y= y'= Sin x Cos x **Cos x -Sin x Tan x Sec2 x **Cot x -Csc2 x Sec x Sec x Tan x **Csc x -Csc x Cot x **Tips: Derivitaves of the “co” functions are always negative!
    • How to use these Derivatives THE BASICS s Let’s look at this equation: s y = 2 sin x - tan x (find y’) x SOLUTION: Find the derivative of s sin x and tan x y = 2 sin x y = tan x y’= 2 cos x y’= sec2x Put them together to get the answer: x y’= 2 cos x - sec2x x
    • How to use Derivatives of Trig. Function(contd.) PRODUCT RULE: s x 4- x2sin x SOLUTION: s 1st, take derivative of each, derivative of 4 and derivative of -x2sin x y=4 y = -x2sin x [must do product rule!] y’= 0 y’= (u + v’) + (v + u’) = (-x2 * cos x) + (sin x * -2x) y’= -x2cos x - 2x sin x
    • How to use Derivatives of Trig. Functions (contd.) QUOTIENT RULE s • [to find y’, use quotient rule: cot x ( lo * d h i )  ( h i * d lo ) ] 1  cot x ( lo ) 2 Solution: s (1 +cot x * -csc2x)-(cot x * - csc2x)/ (1 + cot x)2 = -csc2x - csc2x cot x + cot x csc2x/ (1 + cot x)2 = csc2x(-1-cot x + cot x)/ (1 + cot x)2 ANSWER: s y’ = -csc2x / (1 + cot x)2
    • T H E E N D!!!!