Find x' for x(t) defined implicitly by x + t x + to - 3=0 and then evaluate x' at the point ( - 1, -2). Note that the order of the coordinates in the ordered pair is (t,x). X'= X'| ( -1,-2) = (Simplify your answer.)Find y' and the slope of the tangent line to the graph of the equation below at the indicated point. V20 + y2 - x3 + 58 =0; (4,4) y'= y'| (4,4) = 72 (Simplify your answer.)The demand x is the number of items that can be sold at a price of $p. For x= 14,000-p* , find the rate of change of p with respect to x by differentiating implicitly. The rate of change of the price p with respect to the demand x isThe demand x is the number of items that can be sold at a price of $p. For x= \\9,000- p" , find the rate of change of p with respect to x by differentiating implicitly. The rate of change of the price p with respect to the demand x isGiven : H = 3 9000 - p3 de . d = (9000 - p3 ) 13 - 0 The rate of change of p with respect to a is de ( derivative of p with respect to x). dx Now differentiate O with respect tor. d x = d ( 9000 -p3 ) /3 dx dx = ) 1 = (9000 - p3) 3- (0 - 3 p 2. dp, da dx 1 = 2. (9000 - p3 ) 43 . ( - 3 p 2 dp 1 = _ p2 dp (9000 - p3 ) 7/3 90oo - p3 1 43 = - p2 dp .: multiply both sides by 1 ( 9000 - p3 ) 3/ 3 = ) de - - (90oo- p3 ) 2/3 S. divided both sides by p2 - p2 dP 31 ( 9000 - p 3 ) 2 p2