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1MC3 Assignment # 7 For all problems, use Table of Derivatives and Rules of Differentiation 1. Differentiate and simplify your result: a. f(x) = arccos v2x b. f(1) = tan '(t) + tan '(1/t) c. y = sin(esin ) 2. Find f' for f (x) = Vix+ (x+sin4x)213 +1 ) ex 3. Use logarithmic differentiation to find the derivative of a. f (x) = (sin x)3x- b. y = (cosx) In x 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = x- Vx e* sin x 1 -x x 1/3 _9 b. y = 2x2 - x-1 c. y = tan ("tan"?" means inverse tan) d. xy'+ sec(xy) = by e. y= csch(sin(2v/x)) f. y = (x)sin5x g. y= x2x. h. y = tan (x - VI+ x i. xsin 2y + ysin 3x =5 j. xy - y' sin 2x = Inx+ y 5. Find the equation of the tangent line and the normal line to the curve 4x -5 -1 a. y = - when x = 2; b. y = at the point (1,1) . x+1 X 6. A particle moves according to a law of motion s() =13 -12/ + 361, 1 2 0, where t is in seconds and s in meters. (a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in positive direction? (e) Find the total distance traveled during the first 8 s. (f) Draw a diagram illustrating the motion of the particle. (g) Find the acceleration at time t and after 3 s. (h) Graph the position, velocity and acceleration functions for OSt $ 8. (i) When is the particle speeding up? When is it slowing down? 7. The height in meters of a projectile shot vertically upward from a point 2 m above the ground level with an initial velocity of 24.5 m/s is h = 2 + 24.51 -4.9t- after t seconds. (a) Find the velocity after 2 s and after 4 s. (b) When does the projectile reach its maximum height? (c) What is that max height? (d) When does it hit the ground? (e) With what velocity does it hit the ground