I need help for this problem so that i can understand the next example problem. Thank you

4. For each of the following functions, find the derivative. Use the derivative rules you learned as needed. (9 pts each) f(z) = (1 32)'11 + Jrsin(4-z) g(x) = tan6 2x h(z) = V 1 + 3222 y = 23in (ZxS) y=1n(x83x2+5) {Den 9'? Consider the hyperbola with equation x2 y2 = 1. a. Graph the hyperbola. There are two points on this curve where x = J? Find their (x, y) coordinates. (5 pts) b. Pick the point from part a) with positive ycoordinate, and find an equation of the line tangent to the hyperbola at this point. (10 pts) Use implicit differentiation to find the derivative of y with respect to x if x2 + x2312 + y3 = 3. (10 pts) 2 _ Use logarithmic differentiation to determine f'(x) if f(X) = 3 '0:ng (10 pts) 5. One end of a 13-foot ladder is on the floor, and the other end rests on a vertical wall. a. If the bottom end is being drawn away from the wall at the rate of 3 feet per second, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 5 feet from the wall? (10 pts) b. How fast is the angle of elevation 6 of the ladder changing at that instant? ' (10 pts)