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Product and Quotient Rule Practice 1 1. Let’s try to apply these rules. Find the derivatives for each of the following. a. f(x) = x2sin(x) b. y ln(x) 2x3 c. f(x) = excos(x) d. f(x) 4x3 (x2 4x) 2. y = xsin(x) – 2xcos(x), determine dy . dx 3. Determine each of the following. a. Find f’(x) if f(x) = 4x 3 sin( x) b. Find h’(2) if h(x) = 5x3 – 2x2 4. Determine the derivatives of each of the following. a. y = 5sin(x) b. y = 5xcos(x) c. y = 5sin(x)cos(x) 6. Use the table to answer the given questions. Show your calculus!!!! x f f’ g g’ a. If h(x) = f(x)g(x), determine h’(5). 2 5 -3 2 -1 2 1 2 3 3 4 -2 b. If p(x) = 3x g(x) , determine p’(2). c. Determine the equation of the line tangent to the graph of g(x) at x = 2. 7. Let’s try to apply this rule. Find the derivatives for each of the following. a. f(x) 5x 2 x2 1 b. f(x) sin x x2 4 c. f(x) ex sin x 8. Use the table to answer the given questions. Show your calculus!!!! x f f’ g g’ g(x) 2x 2 5 -3 2 -1 a. If p(x) , b. If p(x) , determine f(x) f(x) 3 determine p’(2) p’(5). 1 2 3 4 -2 2 --------------------------------------------------------------------------------------------------------------9. If f(x) = tanx, determine f’’(x) 10. If f(x) = cotx, determine 3f’(x) --------------------------------------------------------------------------------------------------------------11. If f(x) = secx, find dy at x = dx 4 12. If f(x) = cscx, find 13. Determine the equation of the tangent line of f(x) = sinx, at x = . 3 d2y dx