1) (15 pts) Find the following derivatives: (Show all of your work) a) & ( 5 *+ !) b) - [sin(2x) . cos(5x + 1)] c) (ex - ex) d) [1+2x dx (3-4x]2) (15 pts) Find the derivative of the functions listed below: (Show all of your work) a) Inx' b) exinx c) cos (Inx) 3) (10 pts) a) Find the slope of the line tangent to f (x) = In x at the point (e, 1) b) Find the slope of the line tangent to g (x) = e* at the point (1, e). c) How are the slopes of f(x) and g (x) at these points related?4) (15 pts) A 10 ft long ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/sec, how fast is the top of the ladder sliding down the wall when the ladder is 6 feet from the wall?5) (15 pts) For the equation x2 + 5y? = 45 , find a) by differentiating implicitly b) by differentiating explicitly c) Evaluate -~ from part a) and part b) at the point (5, 2).6) (15 pts) For the equation vx + vy = 5, find x a) by differentiating implicitly b) by differentiating explicitly c) Evaluate -~ from part a) and part b) at the point (4, 9).7) (15 pts) Use implicit differentiation to prove that the line tangent to the circle x2 + y? = r at any arbitrary point (x, y) is perpendicular to the line that passes through (0, 0) and (x, y)