In Exercises 21–42, find the derivative of y with respect to the appro- priate variable. 21. y = cos(x²) 23. y = sin-lV2t 22. y = cos(1/x) 24. y = sin(1 – t) 25. y = sec-l(2s + 1) 26. y = sec-15s 27. y = csc-(x² + 1), x> 0 28. y = csc-1 sec-, 0 <1< 1 29. y = 30. y = sin 31. y = cot Vi 33. y = In (tanlx) 32. y = cotl Vi – 1 34. y = tan¬ (In x) 35. y = csc-'(e') 36. y = cos¯'(e¯") 37. y = sV1 – s² + cos¯ls 39. y = tan¬l vx² – 1 + csc-1x, 38. y = Vs² - 1 sec-ls x > 1 40. y = cot 41. y = xsinx + Vĩ – x² - tan¬lx 42. y = In (x² + 4) – x tan IN MI2

How do I use the chain rule to find the derivative of (y=(cosx+2sinx)8)? I know (cosx=1) and (sinx=0), how do I solve with 2 in front of sinx? Do I apply the (x8) to both (cosx) and (2sinx)? Thank you so much.

2. Fill in the blanks. (1) If f(x)=√x+3, g(x)=x², then (fog)(x)= (2) The differential of the function f(x)=tan(cos .x) is_ (3) The equation of the tangent line of y=x-2x+3 at point (2,3) is_

2. Find the derivative of y in each case. (a) y = sin³x + cos³x (b) y = tan² (x³) (c) y 4 sec(5x)