( t) − 7 determine all the points where the object is not changing. For problems 7 – 16 differentiate the given function. For problems 1 – 6 evaluate the given limit. Section 3.5 : Derivatives of Trig Functions. Thankfully we don’t have to use the limit definition every time we wish to find the derivative of a trigonometric function - we can use the following formulas! Notice that sine goes with cosine, secant goes with tangent, and all the “cos” (i.e., cosine, cosecant, and cotangent. Let’s prove that the derivative of sin (x) is cos (x). TRIGONOMETRIC DERIVATIVES AND INTEGRALS STRATEGY FOR EVALUATINGRsinm(x) cosn(x)dx (a) If the powernof cosine is odd (n=2k+ 1), save one cosine factor and use cos2(x)=1 sin2(x)toexpress the rest of the factors in terms of sine: sinm(x) cosn(x)dx=Z sinm(x) cos2k+1(x)dx= sinm(x)(cos2(x))kcos(x)dx sinm(x)(1 sin2(x))kcos(x)dx 1du 10.(tan1(u)) =dx1 +u2dx 11.Same idea for all other inverse trig functions Implicit Differentiation Use whenever you need to take the derivative of a function that isimplicitlydefined (not solved fory).Examples of implicit functions: ln(y) =x2 x3+y2 = 5,6xy= 6x+ 2y2, etc. Derivative of trig functions cheat sheet Easy way to remember derivatives of trigonometry ratios shorts how to remember derivatives easily
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