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...Chapter derivatives of inverse trig functions urgoalissimple and the answers will come quickly we derive six onewderivativeformulasforthesixinversetrigonometricfunctions d h i dx sin x tan sec cos cot csc theseformulaswillowfromtheinverserulefromchapter page hf f sine cosine applying rule with yields are almost there just have to simplify in denominator do this recall angle for which thussin it is between a z triangle on unit circle whose opposite side be causesinofthisangleequalsx thencos isthe lengthoftheadjacentside bythepythagoreantheorem p thissidelengthis puttingcos into above equation get or latest hsin wereviewedsin section presented its graph figure repeats along derivative from y function derivativeis alwayspositive reecting fact that tangents positive slope has vertical asymptotes at as become increasingly steep approaches nowconsider below havenegativeslope andthegeometrysuggeststhatitsderivativeisnegative indeed turns out exactly case s exercise asks you prove our next tan...