6. Find the derivative of the given function. (You need not simplify your answers.) a) h(x) = x x3 b) r(x) = vx+ c) f(x) = x3 sin x - 4 cotx + 2 d) g(x) = 3csex x2-2 e) k(x) = tan(2x4) 7. Find the derivative of the given function. (You need not simplify your answers.) a) y = (3x2 - 2x - 1) (3x - 2)6 b) y = 4+4) 5 3x-1 c) y = (ex sec x)3 8. Find where the given function has a horizontal tangent. a) f(x) = -3x2 - x b) g(x) = x + sin x (on the interval [0,2x]) c) h(x) =3x4 -6x2 -89. Find each derivative using implicit differentiation. (You need not simplify your answers.) a) Lety = f(x). Find dy/dx for 2x2 + xy - y2 = 2 b) Let x = g(y). Find dx/dy for 3xy + y = 4 - x c) Lety = f(x). Find dy/dx for sin(x + y) = yz cosx d) Letr = h(0). Find dr/do for 04 + 20r2 = 30r 10. Find day/dx2. (You need not simplify your answers, though you may wish to simplify dy/dx). a) x3 - y3 = 7 b) x4 = 2xy c) x4 + 2yz = 3xy11. Write the equation of the tangent and normal lines for each curve at the given point. a) f (x) = x; x =-2 b) f(x) = (4-2x2)3; x = 1 c) x2 + xy + y2 = 1; P(2,3) d) y = 2 sin(nx - y); P(1,0) 12. Find the derivative of the given function. (You need not simplify your answers.) a) y = 3xe5x + In - b) y = Ins (3x-6)5 V2x2+1 ex c) y = 1-sin x d) f(x) = In(tan(5x)) e) g(x) - 3 (3x2-6)*(x-3)2 (8x-3)3 13. Find the derivative of the given function. (You need not simplify your answers.) a) y = sin 1 b) f (t) = cot-1 vt - 1 c) y = arctan v3x2 - 5 d) g(x) = x arccosx + v1 - x2