1. Find the derivative of f (x) = ( Answer. f'(x) = 3x (2x2-1)1(2x6-3x'+6x]-1) (1-x4)* 2. Evaluate the derivative of y = (2x3-x2+1)* 2 dy -16x(3x-1) Answer d (2r)-x3+1)' (2x+1)2 3. Determine the derivative of y = = (3x-1)3 Answery' = (2r+1)(3x-1)(6x+13) (3x-1) 4. Evaluate f (*)(3), if f(x) = 1-x Answer: f() (3) = - 5. Determine the second derivative of 3x2 - 2xy + y? = 1 with respect to x. Answer: y" = ox -4xy+zyl (x-y)> 6. Let f be a twice differentiable function satisfying f(x) = f(x2) -x2. Determine the value of f'(1) and f"(1). Answer: f'(1) = 2 and f"(1) = =2 7. Find the derivative of the function defined by f(x) = Jx + vx + vx Answer: f'(x) = 2 r+vrtvx (1+ 27) 8. Let f (x) = x5 and g(x) = 2x - 3 a. Find (f . g)(x) and (f . g)'(x) b. Find (g . f)(x) and (g . f)'(x) Answer: (a) (2x - 3)5, 10(2x - 3)* (b) 2x5 - 3, 10x4 9. Find f'(x), a. f(x) = (x3 + 2x)37 Answer: 37(x3 + 2x)36(3x2 + 2) b. f ( x ) = (x3 - 2) -2 Answer: -2 (x3 - 7) (3x2 + 2) c. f (x) = = (3x3-2x+1)