Differentiate. g(x) = x*(9.2)* g'(x) =\fEvaluate the derivative of the following function. 2 f(y)=cot_1[ 2 ] Y +2 Choose the correct answer below. , '4Y if} A. f (Y) = 4 2 ' y +4y +8 4y f} B. f'(y)= W ' y +4y +8 _ 4y {}c.fTw='3 ' y + 4y + 8 4y {I} D. f"(W = y2+4y+8 A rectangle initially has dimensions 3 cm by 8 cm. All sides begin increasing in length at a rate of 5 cm/s. At what rate is the area of the rectangle increasing after 18 s? E After 18 s, the area of the rectangle is increasing at a rate of I: V Water is drained out of an inverted cone. having the dimensions depicted in the gure below. If the water level drops at Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V 8 ft/min, at what rate is water (in ft3/min) draining from the tank when the water depth is 3 ft? and \"- , 7 (Type an exact answer, using 1: as needed.) 4 Differentiate both sides of the equation with respect to t. a _ I ' dV ( dh 8 dt dt (Type an exact answer, using 1: as needed) When the water depth is 3 , water is draining from the tank at a rate of V (Type an exact answer, using 1: as needed)