dy An ellipse is represented by the equation a + 2y = 1. Which of the following equations represents O dy 2y O B. dy 2y I O C. dy 21 y O D. dy 2y OE. dy 2y di =Which of the following equations represents the derivative of y = In (x2 + 3x)? O A. y' = 1 O B. (2x+3) (r2 +3x) O C y' = In(21+3) (2z+3) O D. y' In(2x+3) (x2+3x) O E. y' = (2x + 3) In (x2 + 3x)Which of the following equations represents dy ify = xitlo O A. dy x In a O B. dy O C. dy +xInc I O D. dy +1 + x Inc dr O E. dy + IncWhich of the following expressions is y' given that y = sin 22+1 )? O A. y' = COS O B. y' = - COS O C. y' = (121) COS 1 O D. y' = (1) COS O E. ' = ( 3x-41 COSA curve is defined by the equation a try? = y + x y. What is the slope of the graph of the equation at the point (1, 1)? O A. dy = -2 O B. dy dr = -1 O C. dy = 0 O D. dy dr =1 O E. dy = 2Which of the following equations represents dy where y = sin-1 (Vr)? O A. dy di O B. dy 1 2,EV1-12 O C. dy = O D. dy 2 VIVI-12Which of the following equations represents y" when y = e-I'? O A. y" = (-2x) e-x2 O B. y" = (-2x) e-2x O c. y" = - (4x + 2) e-2x O D. y" = - (4x2 - 2) e-2 O E. y" = (4x2 - 2) e-12The position of a particle moving along a line can be modeled by the function s (t) = (2t + 1)* where s (t) is the position of the object in millimeters after t seconds. What is the object's acceleration at t = 0.25 seconds? O A. 27 mm/s O B. 72 mm/s O C. 108 mm/s O D. 121.5 mm/s2 O E. 81 mm/sWhich of the following equations represents the second derivative of y with respect to x for the function defined by x' ty- = x- y? O A. d'y (1-21) da-2 = (1+2y) O B. dy (1+2y) da-2 (1-2x) O c. dy = 4. (1+2y) da-2 (1-2x) O D. day -2 (1+2y) +(1-2x)2 da-2 = (1+2y) O E. d'y da2 = 2 (1+2y) +(1-2x)2 (1+2y)3Which of the following values represents (f-1) (9) where f (x) = a* + 1? O A. (f 1) ' (9 ) = 1, O B. (f 1)'09) = 4 O C. (f-1)' (9) = 0 O D. (f-1)' (9) = 2 O E. (f-1)'(9) = 12Which of the following equations is the derivative of y = =? O A. dy O B. dy O C. dy = 2x In (x) 27 O D. dy = (2In (x) +1)er O E. dy d = x (2In (x) +1) 27What is the equation of the tangent line to the curve y+ Inx = 11 at the point (e-, -3)? O A. y+3 = 1 6e2 (x - e2) O B. y - 3= 1 Be2 (z+ e? ) O C. y - 3 = - 1 6e2 (@ + e2 ) O D. y + 3 = - 1 be2 (x - e2) O E. y+3= -6e2 (x - e2)