G Prove the Leibniz rule for f ( n ) ( x ) , f(n)(x), where f ( n ) f(n) is the n nth derivative of f ; f; that is, show that ( f g ) ( n ) ( x ) = n ∑ k = 0 ( n k ) f ( k ) ( x ) g ( n − k ) ( x ) .

Dean and karlene get paid to write songs. dean is paid a one-time fee of $20 plus $80 per day. karlene is paid a one-time fee of $25 plus $100 per day. write an expression to represent how much a producer will pay to hire both to work the same number of days on a song.