![]() 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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