Which of the following expressions is the derivative of y = cos (In (x + 2))? sin (In(r+2)) O A. y= - O B. sin(In(r+2)) = O C. y' = - sin O D. y' = cos 1 sin (In(x+2)) O E. y=Which of the following expressions is y' if y = cos ? O A. (2x-1) = sin (x-1) I- O B. y = 1 T sin (x-1)2 I- O Cy =- 1 sin (x-1) T-I O Dy' = I (1-1) sin O E y = (2x-1) (x-1)2 sin I-dy Which of the following expressions represents if x and y are related by the equation sinc + siny = x2 +y?? O A. dy 21-COS I 2y-cosy O B. dy 21 + COS I = 2y + cos y O C. dy 2y-cos y dr = 21-COS I O D. dy 21-COS I 2y-cos y O E. dy 21 + COS I dx 2y +cos yWhich of the following expressions is the derivative of y = (va 2 n-1 O A. dy = + 75 dx n-1 O B. dy + (3 7 + 5V13 dx n-1 O C. dy = + (V3x + V513 n-1 O D. dy = n + (V3x + V512) n-1 O E. dy nWhich of the following expressions is y' given that y = sin (x - 1) (x+1) ? O A. y' = -(x -3) (x - 1) cos (x - 1)2 (x + 1)] O B. y' = -(3x - 1) (x - 1) cos (2 - 1)2 (x + 1)] O C. y' = - (x+3) (x -1) cos (x - 1)2 (x + 1)] O D. y' = (3x + 1) (x - 1) cos (x - 1)2 (x + 1)] O E. y' = (3x - 1) (x - 1) cos (x - 1)2 (x + 1)]Which of the following expressions represents y' when sina + cosy = sin (x2) + cos (y?)? O A. 2x sin (x2) -sinc y = 2y cos(y?)-cos y O B. 2x sin (x2) +sinx y' = 2y cos(y?) + cos y O C. 2x cos (12) -COS I 2y sin(y-)-sin y O D. y' 2x cos (x2) + COS I 2y sin(y?) +sin y O E. 2y cos (y-) -cosy y = 2x sin(2) -sin cA curve is defined by the equation cosa = y - a2. Which of the following values is the best approximation of the slope of the line perpendicular to the graph of the equation at the point (,, " ) ? O A. -1 O B. 1 OCT O D. IT2 O E. 1+TGiven that In y = x + y, which of the following expressions is equal to dx2 O A day 1 da-2 (1- O B. d'y H da-2 (1-y) O c. dy y da2 (1- O D. dy 1-2y da-2 (1-y)- O E dy (1-2y)y da2 = (1-y)3dy Which of the following expressions represents where y = tan (x2 + 1)? O A . dy O B. dy 21 = 1421241 O c. dy 21 12+ 21+2 O D. dy I +21-+2 O E. dy I +2x-+1 21Which of the following expressions represents y' when y = esin'? O A. y' = 2 sin I COS I O B. y' = (esin' x ) sin & cos x O C. y' = 2 cos (esin z ) O D. y' = (2esin' x ) sin x cos i O E. y' = - (2esin' x ) sin x cos rWhich of the following expressions represents the second derivative of y = In (ex te )? O A. d'y da-2 = ( exte z)2 O B. dy 4 ( exte z)2 O c. d'y (ex -e-I) da-2 ( exte I) O D. dy 2(ex te 20 ) da-2 = (exte z)2 O E. d'y 1(e2T te 2 ) = da2What is the equation of the line that is normal to the curve y? | 111:1? : 19 at the point (23? 4)? Given the curve defined by the equation In (x - 1) = ax - by, which of the following values represents the value of a if the curve goes through the point (2, 1) and the line tangent to that point has a slope of 1? O A. a = - O B. a= - 1 12 O C. a= 1 12 O D. a = O E. a= to| kWhich of the following values represents the value of the second derivative of y with respect to x for the function defined by In (@y) = x - y at the point (1, 1)? O A. d'y da-2 = O B. dy da2 = O c. dy da-2 = 0 O D. d'y da-2 O E dy da-2Which of the following values represents (f-1 ) ( - - where f (x) = (3x - 1)37 O A. - O B. O C. O D. O E. -Given that yz = xy, which of the following expressions equals dyn O A. dy r(c-ylx) y(y-x Iny) O B. dy r(r-ylny) y(y-rlnx) O C. dy x(y-xlny) y(x-ylnc) O D. dy y(x-ylny) x(y-rlx) OE. dy y(y-rlny)The position of an object moving along a line can be modeled by the function s(t) = kt - 0.81(1 - t?)"where s (t) is the position of the object after t seconds after the object is thrown and k is a constant. What is the object's velocity as a function of time? O A. v(t) = k - 0. 81t(1 - (2)2 O B. v(t) = t - 0. 81t(1 - 2) 2 O C. v(t) = k + 4. 86t(1 -+2)2 O D. v(t) = k + 4.86(1 -(2)2 O E. v(t) = k - 4. 86t(1 -2)2You are given a function f (a) and told that the function g (x) = af(), a > 0, has a slope equal to 2 In a at x = 0. Which one of the following functions could be f (a)? O A f(x) =12 O B. f(x) = ex - 1 o c. f(x) = 2x2 + 4x O D. f(x) = 2 cos (x) - 2 O E. f(x) = 2In (x+1)What is the x-intercept of the line tangent to the graph of y? = x2 + y at the point ( -V6, 3)? O A. V6 12 O B. O C. 2V6 5 O D. V6 4 O E. 2V6 5You are given the functions f (x) and g (x) = sin (f (x)) Which of the following expressions represents the ratio of the derivatives of these two functions, f'(I). g'(I) ? Assume that the domain of g (x) is 7 E f ( 2 )