(a) Show carefully how to use the rules of logarithms given in lectures to deduce that ln(x3x+1) = (3x + 1) ln(x) whenever x > 0. State which rule(s) you are using in general form.

(b) (c)

Giving full details of all steps, show how to use the product rule for derivatives to find the derivative of (3x + 1) ln(x).

Show how to find the derivative of x3x+1 by first writing it in a different exponential form and then using the results of parts (a) and (b) above. State which rules you use along the way.