Expression 5: StartFraction, "k" plus cos left parenthesis, 2 "x" , right parenthesis Over StartRoot, 1 plus "k" squared plus 2 "k" cos left parenthesis, 2 "x" , right parenthesis , EndRoot , EndFractionk+cos2x1+k2+2kcos2x
5
dy/dx =
6
Expression 7: StartFraction, 2 left parenthesis, 1 plus "k" cos left parenthesis, 2 "x" , right parenthesis , right parenthesis Over 1 plus "k" squared plus 2 "k" cos left parenthesis, 2 "x" , right parenthesis , EndFraction StartFraction, abs left parenthesis, "k" plus cos left parenthesis, 2 "x" , right parenthesis , right parenthesis Over "k" plus cos left parenthesis, 2 "x" , right parenthesis , EndFraction21+kcos2x1+k2+2kcos2xabsk+cos2xk+cos2x
7
Expression 8: "y" equals arc sine left parenthesis, StartFraction, sin left parenthesis, 2 "x" , right parenthesis Over StartRoot, 1 plus "k" squared plus 2 "k" Subscript, 0 , Baseline cos left parenthesis, 2 "x" , right parenthesis , EndRoot , EndFraction , right parenthesis left brace, 0 less than or equal to "x" less than or equal to StartFraction, pi Over 2 , EndFraction , right bracey=arcsinsin2x1+k20+2k0cos2x0≤x≤π2