9. The derivative of y a) 2e*sin(x) = 2cos(x) e . 10. Given f(x) = a) 4 b) 2e* cos(x)sin(x) sin(4x+), find f'() c)2e* (cos(x) – sin(x)) d) 2e*cos(x) + 2e*sin(x)) b)- 4 c) 0 d) 1
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- Find derivatives of the functions defined as follows. y=e-x2B: Find the derivative of each of the following function a) x²- xy = cos y b) y=√1-sin³ (5x)) d) y = tan² (¹) e) sin (y)= x² + cos² (x) c) y === D) y = (-1) (x³ +4x)Find the derivative of y = x°eX. O a. y' = 3e*x2(eX + x) O b. y = 3x2(e* + 1) O c. y = e*x²(x +3) O d. y = 3×2EX + 3eX Find the derivative of y = (1 - cos 2x)“. O a. y' = (8 sin 2x)(1 - cos 2x) %3D O b. y' = (8sin 2x)(1 - cos 2x)3 O c. y= (4 sin 2x)(1- cos3 2x) O d. y' = (4sin 2x)(1 - cos 2x)3
- 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception occurs in each case? (a) Incorrect: f'(x) = (– sinx)(3x²) + (cos x) (6x). (b) Incorrect: f'(x) = – sin(6x).2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1 2. f(x) = csc x + 2x + x³. x cos x 3. f(x) = 6+2xWhat is the derivative of x 3 sin(x)? Select one: -(sin(x) + 3xcos(x)) 2 Зх 3 1 + cos(x) 2 Зх 3 1 O 3x sin(x) + x³ cos(x) cos(x) Зx 3
- Find the third derivatives of the function f (x) = e" sin (2x) O-1le" sin 2x + 2e" cos (2x) O-1le" sin 2x – 2e" cos (2x) 11e" sin 2x – 2e" cos (2x) -3e" sin 2x + 4e® cos (2x)Let F(x) = sin(x) ex a) Find f'(x), F"(x), f(3) (x), FC (X) b) Find f (27) (x), the 2n-th derivative OF F(X) (n is a positive integer)8) Find the derivatives of the following: a) f(x) = 4e* – 2x + 5 | b) f(x) = In 2x2 c) f(x) = (4 – x)5