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EMBED Equation.DSMT4  (a) If  EMBED Equation.DSMT4  Recall  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  So  EMBED Equation.DSMT4  (b) Use implicit differentiation to get the derivative of the inverse of  EMBED Equation.DSMT4  Exchange the x and the y to get: x = Sin y. Take the derivative w.r.t. x:  EMBED Equation.DSMT4 . Now we pull out that Rt Triangle Trick Trick! If sin y = x, what is cos y = ? (See figure below) cos y =  EMBED Equation.DSMT4 =  EMBED Equation.DSMT4    dy/dx = 1/cos y or  EMBED Equation.DSMT4  Derivatives of Inverse Functions Notes (2) 3. Given  EMBED Equation.DSMT4  with  EMBED Equation.DSMT4 , (a) Find  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and then well use:  EMBED Equation.DSMT4  to get:  EMBED Equation.DSMT4  (b) Use implicit differentiation to find  EMBED Equation.DSMT4  To find the inverse function for y = Tan x, we exchange the x and the y to get:  EMBED Equation.DSMT4  and then we take the derivative w.r.t. x to get:  EMBED Equation.DSMT4  and then we use the rt  EMBED Equation.DSMT4  trig trick:   4. Derivatives of the other Inverse Trig Functions  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  both of which can be proven by taking the derivative w.r.t. x of the trig identities:  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  We dont worry too much about Inverse Secant and Inverse Cosecant since we can Always use the following identities involving Inverse Cosine and Inverse Sine:  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  By the way this doesnt quite work for Inverse Cotangent, since:  EMBED Equation.DSMT4  ex/  EMBED Equation.DSMT4  but ex/  EMBED Equation.DSMT4   EMBED Equation.DSMT4  So if Tan y = x, then  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  (,-01HIJKWXopqrs{ܼܕ܊}rgZrj hzt h}UEHUjG h}UUVh?h}UCJaJjhzt h}UEHUjG h}UUVhJh}UCJaJjhzt h?EHUjG h?UVh?jh?Ujhzt h}UEHUjG h}UUVh}Ujh}UUh@CJaJhD;<CJaJh}UCJaJ#-Mt7 # |  B  x M c''hC'|'hC'І'#''''''#''hC't;'m' '''(]''{'t;'t;'gd2$a$gd2gd}U$a$gd}U|   3 4 5 6 = ? @ A X Y Z [ _ f g h  ; < Ÿ󔜉|qeq]hJCJaJhJhJCJH*aJhJhJCJaJjhzt hJEHUjG hJUVjhJUhJjhzt h}UEHUjMG h}UUVjVhzt h}UEHUj.G h}UUVhJh}UCJaJjd hzt h}UEHUjG h}UUVh}Ujh}UU$< S T U V X        " # & ' > ɼԳtld`h?jh?Uh?CJaJh?hJCJaJh]%j#hzt hJEHUjiG hJUVjhzt hJEHUj G hJUVhJCJH*aJjhzt hJEHUj^G hJUVhJCJaJjhJUjhzt hJEHUjG hJUVhJ"> ? @ A B K R S j k l m n r s        ! 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