1. A ladder 25 feet long is leaning against the wall of a house The base of the ladder is pulled away from the wall at a rate of 2 feet per second. a) How fast is the top of the ladder moving down the wall when its base is 7 feet from the wall? b) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall. (Assume the angle is measured in radians.) 2. Differentiate the following: a) f(t) = 6(t-+in(t)) b) g(x) = log,, (sin(x + 2)) c) y = In(3x + 1) cos-1(x3) 3. Find the equation of the tangent line to the curve f(x) = In(e2x + cos(2x) ) at the point (x, y) = (0, In(2) ) 4. Use logarithmic differentiation to find derivatives of the following: a) y = (3x + 5)" b) y = In(x)tan(x) Note: "arc" is another way to denote the inverse trig functions. So sin (x) = arcsin(x), for example