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MACH5 Extra Credit PowerPoint

MACH5 Extra Credit PowerPoint. Dean Bates P.3 11-7-2009. t oday’s topic…. d erivatives of trig functions. Basic Problems. derivative sin(x) = cos (x) derivative cos (x) = -sin(x) derivative csc (x) = - csc (x)cot(x) derivative sec(x) = sec(x)tan(x) derivative tan(x) = sec 2 (x)

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MACH5 Extra Credit PowerPoint

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  1. MACH5 Extra Credit PowerPoint Dean Bates P.3 11-7-2009

  2. today’s topic… derivatives of trig functions

  3. Basic Problems • derivative sin(x) = cos(x) • derivative cos(x) = -sin(x) • derivative csc(x) = -csc(x)cot(x) • derivative sec(x) = sec(x)tan(x) • derivative tan(x) = sec2(x) • derivative cot(x) =-csc2(x) NOTE: derivatives of sin, sec and tan are positive; derivatives of cos, csc and cot are negative

  4. More Complex Problems • “derivative sin(x) = cos(x)” really means: • derivative sin (x) = d(x)cos(x) times the result of the power rule for sin(x), which equals (1)(1)cos(x) or cosx • the same is true for the other trig functions • So, derivative 3sec(x2) = 6xsec(x2)tan(x2), and so on. • now for a quiz…

  5. Questions • 1.y=3sec2(x) • 2.y=[cos(x)] / x2 • 3.y=cot3(x) • Answers • 1.d(x)=3(1)[2sec(x)][sec(x)tan(x)] or6sec2(x)tan(x) • 2.d(x) =[-2xsin(x)-xcos(x)]/x4or [-2sin(x)-cos(x)] / x3 • 3.d(x) =3(1)[csc2(x)][cot2(x)] or3csc2(x)cot2(x) Get it? If not, then re-read the previous slide. Still don’t get it? Try Rastafarianism.

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