MA 241 Calculus 1 Answer Key: Practice Problems for Test 2 Fall 2022 1. 2 x4/5- - 2+ +8ex 2. (a)y' = 1+2_6 14 + 25, (b) y' = 4x3 - 8x , (c) y' = -2 tan 0 sec2 0 3. (a) y' = x(2Inx +1) , (b) y' = 0(2 tan 0 + 0 sec2 0) , (c) y' = x2e *(3 -x) , (d) y' = cos2 x - sin2 x 4. (a) f'(x) = 2(1-x) 3 secx 3ex , (b) f' (x) = (* tanx) , (c) f' (x) = , (d) f'(x) = - csc2 x 5. (a) y' = -- 5 . y" -25 250 3750 4-5x (4-5x) 2 y'll = y(3) = - (4-5x)3 y4)= - (4-5x)" (b) y' = 2 cos(2x) , y" = -4sin(2x) , y'' = y(3) = -8 cos(2x) , y(4) = 16 sin(2x) (c) y' = -2e-2x , y" = 4e-2x , y'll = y(3) = -8e-2x , y(4) = 16e-2x (e) y' = 3x2 - 2 , y" = 6x , y"' = y(3) = 6, y(4) = 0 6. (a) 15x4 sec2(3x5) , (b) 7(18x5 - 8)(3x6 - 8x)6 , (c) - csco cote ecsce , (d) -2 tan(2t) (e) - - 30x2 (5x3_1)s , (f) 45x +1 (In 4) 10x , (g) . (h) ax = x242 2x 2(3x+1)] \x(3x+1) x2 +2 7. (a) dy _ 3-3x ty (b) b) dy _ 1-y sin(xy) 4-x dx 1+x sin(xy) ' (C) -=- 1-2y2+xy (d) dy -10yz+y dx x+y? seczy 8. (a) y = 2x - 8, (b)y = 4x + 1 , (c) y = -x+4 9. 72mr miles?/hour 10. 1/32n m/sec 11. 8/3 ft/sec 12. 46.86 mph 13. (a) = [In(cosx) - x tan x](cosx)* , (b) a = [In(x) + 1]xx , (c) dy = [cos(x) In(x) + sinx] xsinx [In(0)+2]tThe following questions are a suggested list of practice problems to prepare for your test. These questions are not guaranteed to be a complete preparation for the exam, but they can serve as a starting point. You should also refer to your homework and extra worksheets provided by your professor. On the test, you WILL BE expected to fully support your answers using Calculus techniques taught in class. SHORT CUTS will not be accepted as supporting work, but should be used to check your answers only. Practice showing work in an organized, legible manner. 1. Calculate the following derivative. dx 10x5 - 4Inx - 72 +8ex - 1) 2. Find the derivative of the following function. a. y = [-tz+2t-1 by = (x2 - 1)(x2 - 3) c. y = (1 - secx) (1 + secx) 3. Find the derivative of the following function. a. y = x2 Inx b. y = 02 tan 0 c. y = x3e x d. y = cos x sin x 4. Find the derivative of the following function. a. f(x) = 2x 7x _cos x b. f (x ) = 3 secx c. f (x) = 2-1 d. f ( x ) = sin x 5. Find the first 4 derivatives of the following function. a. y = In(4 - 5x) b. y = sin(2x) c. y = e-2x d. y = x3 - 2x 6. Find the derivative of the following functions. (tan(3x5)) day ((3x6 - 8x)?) 28 (ecsco) d. - (In(cos(2t))) e. dx (5x3-1)2 f. d g. - In(5x3) h. y = x2+2 Vx(3x+1)