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 ify = sin (tan 2x) 4. Find ify = In t 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 x-y 9. Find _ ify = 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 Sources: The Princeton Review AP Calculus Prep 2021 and Larson & Edwards Calculus ETF 6e\f16. 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 = 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