Some of these already have answers. Can you just give me a clear explanation without using cursive?

14. Show that the equation cose + -3 =e- has a real root. 15. Use the definition of derivative to find the derivative of f(x) = x2 + 5x. Answer: f'(x) = 2x + 5 7 16. Use the definition of derivative to find the derivative of f (x) = - V5r + 4 35 Answer: f (x) = 2(5.x + 4)3/2 17. Find y'. You do not have to simplify your answer. (a) y = sin(cot x) + (22 + 3)1/3. Answer: y' = cos(cotr) (- csc r) + 2.r 3(x2 + 3) 2/3 ( b) y = + coser + 3 cot x2 1 + 9r Answer: y' (23"In(2)6x - sinx - 6x csc(x2)) (1 + 9r) - (2" + cosx + 3 cot r?) (9) (1 + 9.x)2 (c) y = e' sin(x3 - 2r) - sect Answer: y' = 5e' sin(x3 - 2x) + (3.x2 - 2)5 cos(x3 - 2x) - exec secr tanr Ary Vary - y (d) vary =1+ xy Answer: y' = x - 2x2 fry (e) ysina' = xsing? Answer: y' 2ry cosm' - sin y 2ry cosy2 - sin a2 18. Find an equation of the tangent line to the curve a try-y" -1 =0 at the point (1, 1). Answer: y = 5 - 2 3 19. Find the point(s) on the curvey = 2r" +3x2 -12x+1 where the tangent is horizontal. Answer: (1, -6), (-2, 21)20. Find the values of r in [0, 2x] where the tangent line to the curve y = 2 sinr - 5r is perpendicular to the line x - 4y = 7 Answer: x or T 3