AP Calculus Unit 3 Test (Please show your work) 1. Find ify = (In x) 4 2. Find ~ at (1,3) if y = Vx2 + 8x 3. Find * if y = sin (tan 2x) 4. Find ify = " Int 5. Find the equation of the tangent line to the graph of f (x) = tan x at (" , 1) Sources: The Princeton Review AP Calculus Prep 2021 and Larson & Edwards Calculus ETF 6e6. Find the equation of the tangent line to the graph of f (x) = v2x2 - 7 at (4,5) 7. Find at (1,1) if 16x2 - 16xy + y2 = 1 8. Find " if x - cos(y) = xy dx x - y 9. Find ay if *+2 = 3 at (2,1). 10. Find the slope of the tangent line to the graph of (x2 + y2)2 = 4x2y at (0.5,0.8). Calculate your answer to 2 decimal places. 0.5 0.5 Sources: The Princeton Review AP Calculus Prep 2021 and Larson & Edwards Calculus ETF 6e11. Find if sin x + 1 = cosy 12. Find ~ ify = y3 - x2 13. Find " 2 ify = 5(2 - 7x) 4 14. Find & if daz if y = sin x2 15 . Find " 2ify = (3 + 2x)e-3x Sources: The Princeton Review AP Calculus Prep 2021 and Larson & Edwards Calculus ETF 6e16. Given f (x) = x3 - 1, find the derivative of the inverse function at f-1(26) Hint: You'll need to figure out f (? ) = 26 17. Given f (x) = x3 + 2x - 1, and the graph, find the derivative of f-1(2) Hint: Use the graph to figure out f (? ) = 2 18. Given f(x) = sin x, find the derivative of f-1 at x = NIN 19. Find the derivative of f (x) = arcsin (x + 1) 20. Find the derivative of f (x) = arctan ex Sources: The Princeton Review AP Calculus Prep 2021 and Larson & Edwards Calculus ETF 6e