please answer all the questions correctly with a small explanation for each question :)

QUESTION 1

\fIf f(x) = h(tan(x)), then f'(x) is equal to which of the following? Oh '(sec2(x)) O sec2(x) Oh (tan(x)) Oh (tan(x))(sec2(x))Which of the following is an equation of the tangent line at (2, 5) of 3x- - xy = 2? Oy-5=-(x-2) Oy-5 = - NIN (x - 2) Oy-5--6(x-2) O y-5=5(x-2)\fA particle in rectilinear motion is defined as s(t) = -In(-4t + 4) + cos(2t) for t 2 0 seconds, where s is given in meters. Find the instantaneous rate of change in position, in meters per second, at t = 2. O 0.25 - sin4 O-1 - 2sin4 O 1 - 2cos4 O 1 - 4cos4An airplane's height in feet during an eight-hour flight is given as h(t). Find the expression that represents the rate of change of the plane's height, with respect to time, five hours into the flight. O h(5)-h(0) 5 O Ah 45 Oh "(5) Oh '(5)The amount of medication, in milligrams, in a patient's bloodstream after t hours, can be represented by the following function: 100 M(t) = 1+ ex+0.8 What is the rate of change for the amount of medication in the patient's bloodstream after 3 hours? O-2.1881 mg/hr O-2.1402 mg/hr O -0.0479 mg/hr O 2. 1881 mg/hrThe table of values describes the behavior of decreasing function k{x}. Find the slope of the line tangent to the graph at k'1(1). 1 3 ' 0 Undened due to a {l in the denominator O l 2 What is the derivative of y=(sin-15x2)37 Oy'= V1-25x4 Oy'= 10x V1-25x4 Oy'= 30x(sin-15x2)2 V1-25x4 Oy'= 3(sin 15x2)2 V1-25x4Based on the graph, which of the following guarantees that an estimate using a tangent line approximation will result in an underestimate? ' O A point of tangenqg.r near x = 2 ' O A point of tangency near x = 0 ' O A point of tangency near x = 6 ' O A point of tangency near x = 12 A particle moves along the y-axis such that its position at time t is given by y(t) = to - 6t for t = 0. At what time is the particle speeding up? Of =0 Of = 2 Of = 4 Of = 5Functions x, y, and z are dierentjable with respect to time and are related by the equation x = yr? If y is increasing at a constant rate of 2 units per minute and z is decreasing at a constant rate of 3 units per minute, at what rate is x changing, with respect to time, when y = 4 and z = 5? | 0170 0 770 070 l 0170 A stomp rocket is launched straight into the air and is being watched by students 500 meters away. After 2 seconds, when the angle of elevation is , the angle is increasing at a rate of 0.4 radians per second. How fast is the stomp rocket rising at that moment? O 400 m/sec O 300 m/sec O 200 m/sec O 100 m/secWhat is the missing portion of f ' for f(x) = 20(2x2 - x ) ? V3x3 + sin23x f'(x)= (V3x* + sin (3x))2e(2x