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An object moves along a straight line with position at time t given by s (t) = 3t cost . What is the velocity of the object at time t ? Ov(t) = -12+3 sint Ov(t) = 12+3 cos t - 3t sint Ov(t) = 12+3 sint Ov(t) = 12t3 cost + 3t sintUse the information given in the table to nd the following derivatives. All answers are integers. a) If R(:c) = (tanm) f(:c) then R' ( Mt! V b]|fh(:c )2 253;"; then h'(7r )2 c) If L(as) = if?) then L' (O) = Suppose L is the tangent line of y = 3 tan x - 2 cscx at x = Where does L intersect the x-axis? O At x = 1 V3 8 O At x = V3 8 O At x = 3V3 - A V3 O Atx = 40 O At * = 407T 3A student hands in the following work: Problem: Given that F (11)) = cos(sinw) nd F' (g) . Round your answer to 3 decimal places. Student answer: Line 1: The variable here is 'w , but the method used to differentiate is the same as if the variable had been :1). Line 2: Recall that the derivative of y : cos :1: is y' = 7 sins: and the derivative of y = sin m is y' = cos a: . Line 3: Using the Product Rule, we get: Line 4: F' (10) = sin(sin w) + cos(cos 10) Line 5: To nd F' (g) we need to evaluate Fl (11)) at 'w : %. Line 6: Fl ('7) Z sin (sin g) -l- cos (cos 1) 4 - 1 1 sme)+ws