Consider this function y = f(x) on the domain (-∞, ∞). f(x): = :{ 8 x sin()+ 38 if x = 0 38 X if x = 0 (a) If x 0, f'(x) = || ×

Suppose f(x) = sinx, and let k be a real number. Let F(x) = f(xk) and G(x) = [ƒ(x)]k. Find expressions for (a) F'(x) and (b) G'(x). (a) F'(x) = (b) G'(x) =

Find f'(x) and simplify. f(x)= x x+2 Which of the following shows the correct application of the quotient rule? (x)(1)-(x+2)(1) ○ A. [x]² (x)(1)-(x+2)(1) ○ B. [x+2]² (x+2)(1)-(x)(1) C. [x+2]² (x+2)(1)-(x)(1) ○ D. [x]² f'(x) = ☐

Let f(x) and its linear derivative f'(x) be defined for all real numbers. Use the table of selected values to determine f(5). x 2 3 4 5 f(x)-1? -13 ? f'(x)-4-6 ? -10 -19 0-22 O-23 O-31

g(x) = 1 + √x

Find f'(x) and simplify. X X - 19 f(x) = Which of the following shows the correct application of the quotient rule? O A. O B. O C. O D. f'(x) = (x)(1)-(x-19) (1) [x - 191² (x-19)(1)-(x)(1) [x-19]² (x)(1)(x-19) (1) [x]² (x-19)(1)-(x)(1) [x]²

Find the derivative of the function f(x) = 2x3 – 3x by using the definition of the - derivative.

Let f (x) = x² – 3. a) Use the definition of derivative to find f' (). | (Write your answer in the form f(x)=..) b) Use the definition of derivative to find f" (x). (Write your answer in the form f(x)=..)