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Lecture_3_3-1 - sinx and cosx just derived Find the...

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Lecture 3.3 Derivatives of Trigonometric Functions Optional problems from the text: #1-13 odd, 15,16,19,21,29,31,35,37 To prove the derivatives of y = sin " and y = cos " we’ll need to results of two limits lim " # 0 sin " " = 1 lim " # 0 cos " $ 1 " = 0 Write down, using the limit definition, the derivative of y = sinx Write down, using the limit definition, the derivative of y = cosx Now that we have these two derivatives, we can find the derivatives of the other 4 basic trigonometric functions using quotient rule. Find the derivative of y = tanx using the quotient rule and the derivatives of
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Unformatted text preview: sinx and cosx just derived. Find the derivative of y = secx Examples: 1. Differentiate: a. y = 1 + sin x 3 " cos x b. y = e u (cos u + 5 u ) c. y = t 3 cos t Make sure you work through h/w #15 and #16 which prove the derivatives of cscx and cotx. Copy into your notes to memorize The red bordered box on page 194 of the text Example: #23 page 196 Find an equation of the tangent line to the curve y = 2 x sin x at the point ( " 2 , )...
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