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Knowledge/Understanding Multiple Choice: [ 1. Derivative of f(x) = cos²x a) 2cosx 2. Derivative of f(x) = 7e-4x a) 7e4x 3. Find the slope of the tangent at x a) 2 b) sin²x c) cosx(sinx) d) -2sinx(cosx) b) -4e-4x d) -28e-4x b) = c) -28e-28x = 1 for y ln(2x+3) Π c) 1) 4. Given f(x) = sin² (2x) find the slope at ( a) -√3 b) √√3 c) — 2 5. For y -ln(x), find the value of x where the slope is · a) x=-6 b) -In(6) c) - 160 b) 633x In(3) c) 3(73%)In(3) 6. Find y" give y = 73x a) 213x In(7) χ 7. If f(x) = find f'(−1) a) e b) 2e c) 0 d) In(5) d) 0.1395 d) Does Not Exist d) 9(73%)(In7)² d) 1 | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a) √ex 1 b) 2√e c) -4 d) 1 d) √√√ex b) 3e (cosx)(sinx) c) 3e* (cosx-sinx) d) 3e cosx+3e sinx 10. The derivative of y = 3e*cosx a) 3e*sinx Communication True or False: [' 11. The derivative of a sinusoidal function is another sinusoidal function. 12. The rate of change of a sinusoidal function is periodic in nature. 13. A sinusoidal function can be differentiated only if the independent variable is measured in radians. 14. The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. 15. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. sinx 16. Using the Quotient tanx = to prove tanx = sec²x. [3 Marks] COSX dx

Knowledge/Understanding Multiple Choice: [ 1. Derivative of f(x) = cos²x a) 2cosx 2. Derivative of f(x) = 7e-4x a) 7e4x 3. Find the slope of the tangent at x a) 2 b) sin²x c) cosx(sinx) d) -2sinx(cosx) b) -4e-4x d) -28e-4x b) = c) -28e-28x = 1 for y ln(2x+3) Π c) 1) 4. Given f(x) = sin² (2x) find the slope at ( a) -√3 b) √√3 c) — 2 5. For y -ln(x), find the value of x where the slope is · a) x=-6 b) -In(6) c) - 160 b) 633x In(3) c) 3(73%)In(3) 6. Find y" give y = 73x a) 213x In(7) χ 7. If f(x) = find f'(−1) a) e b) 2e c) 0 d) In(5) d) 0.1395 d) Does Not Exist d) 9(73%)(In7)² d) 1 | | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a) √ex 1 b) 2√e c) -4 d) 1 d) √√√ex b) 3e (cosx)(sinx) c) 3e* (cosx-sinx) d) 3e cosx+3e sinx 10. The derivative of y = 3e*cosx a) 3e*sinx Communication True or False: [' 11. The derivative of a sinusoidal function is another sinusoidal function. 12. The rate of change of a sinusoidal function is periodic in nature. 13. A sinusoidal function can be differentiated only if the independent variable is measured in radians. 14. The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. 15. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. sinx 16. Using the Quotient tanx = to prove tanx = sec²x. [3 Marks] COSX dx

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Knowledge/Understanding Multiple Choice: [ 1. Derivative of f(x) = cos²x a) 2cosx 2. Derivative of f(x) = 7e-4x a) 7e4x 3. Find the slope of the tangent at x a) 2 b) sin²x c) cosx(sinx) d) -2sinx(cosx) b) -4e-4x d) -28e-4x b) = c) -28e-28x = 1 for y ln(2x+3) Π c) 1) 4. Given f(x) = sin² (2x) find the slope at ( a) -√3 b) √√3 c) — 2 5. For y -ln(x), find the value of x where the slope is · a) x=-6 b) -In(6) c) - 160 b) 633x In(3) c) 3(73%)In(3) 6. Find y" give y = 73x a) 213x In(7) χ 7. If f(x) = find f'(−1) a) e b) 2e c) 0 d) In(5) d) 0.1395 d) Does Not Exist d) 9(73%)(In7)² d) 1
Transcribed Image Text:Knowledge/Understanding Multiple Choice: [ 1. Derivative of f(x) = cos²x a) 2cosx 2. Derivative of f(x) = 7e-4x a) 7e4x 3. Find the slope of the tangent at x a) 2 b) sin²x c) cosx(sinx) d) -2sinx(cosx) b) -4e-4x d) -28e-4x b) = c) -28e-28x = 1 for y ln(2x+3) Π c) 1) 4. Given f(x) = sin² (2x) find the slope at ( a) -√3 b) √√3 c) — 2 5. For y -ln(x), find the value of x where the slope is · a) x=-6 b) -In(6) c) - 160 b) 633x In(3) c) 3(73%)In(3) 6. Find y" give y = 73x a) 213x In(7) χ 7. If f(x) = find f'(−1) a) e b) 2e c) 0 d) In(5) d) 0.1395 d) Does Not Exist d) 9(73%)(In7)² d) 1
| | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a) √ex 1 b) 2√e c) -4 d) 1 d) √√√ex b) 3e (cosx)(sinx) c) 3e* (cosx-sinx) d) 3e cosx+3e sinx 10. The derivative of y = 3e*cosx a) 3e*sinx Communication True or False: [' 11. The derivative of a sinusoidal function is another sinusoidal function. 12. The rate of change of a sinusoidal function is periodic in nature. 13. A sinusoidal function can be differentiated only if the independent variable is measured in radians. 14. The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. 15. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. sinx 16. Using the Quotient tanx = to prove tanx = sec²x. [3 Marks] COSX dx
Transcribed Image Text:| | | 8. Given f(x) = sin (4x + 7/7), find f' (Z). a) 0 b) 4 9. The derivative of y = √√ex is: a) √ex 1 b) 2√e c) -4 d) 1 d) √√√ex b) 3e (cosx)(sinx) c) 3e* (cosx-sinx) d) 3e cosx+3e sinx 10. The derivative of y = 3e*cosx a) 3e*sinx Communication True or False: [' 11. The derivative of a sinusoidal function is another sinusoidal function. 12. The rate of change of a sinusoidal function is periodic in nature. 13. A sinusoidal function can be differentiated only if the independent variable is measured in radians. 14. The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. 15. There are an infinite number of tangents with a given non-zero slope to a sinusoidal curve. sinx 16. Using the Quotient tanx = to prove tanx = sec²x. [3 Marks] COSX dx
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