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Unformatted text preview: Functions Find d dx (sin 1 x ). What is d dx (cos 1 x )? ex. Let f ( x ) = sin 1 (2 x 1). Find the following: 1) domain of f ( x ) 2) f ( x ) = 3) domain of f ( x ) Find the derivative of y = tan 1 x . ex. Find f ( x ) if f ( x ) = tan 1 ( e 2 x ). ex. If g ( x ) = x tan 1 ( x ), nd the equation of the tangent line to g ( x ) at x = 1. d dx (csc 1 x ) = d dx (sec 1 x ) = d dx (cot 1 x ) = ex. Two curves are called orthogonal if at each point of intersection their tangent lines are perpendicular. Two familie of curves are orthogonal trajectories if every curve in one family is orthogonal to every curve in the other. Show that the hyperbolas xy = c for c 6 = 0 are orthogonal trajectories to the hyperbolas x 2 y 2 = k for k 6 = 0....
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