Hi guys, any help with the following questions will be very much appreciated! 1. Prove that u(x,y) = ln(x^2+y^2) has a generalised derivative on the unit ball in R^2 (Approximate by smooth functions?). 2. Prove that g.u has a generalised derivative on A if: A is bounded and open in R^n g is a smooth function in R^n u is measurable, u is in L(1)loc(A) and has a generalised derivative on A. (Thinking of using the formula for the derivative of a product of smooth functions?) 3. Construct a smooth function fn on R such that: fn(x) = 1 if x<n (includes equality) fn(x) = 0 if x>n+1 (includes equality) 0<fn(x)<1 for all x in R (includes equality) the derivative of fn is bounded Thanks alot!