Cos'è (f (x + h) - f (x)) / h quando f (x) = x ^ 2 + 9x-3?

# = lim_ (h-> 0) ((x + h) ^ 2 + 9 (x + h) - 3 - (x ^ 2 + 9x - 3)) / h #

# = lim_ (h-> 0) (x ^ 2 + 2xh + h ^ 2 + 9x + 9h - 3 - x ^ 2 - 9x + 3) / h #

# = lim_ (h-> 0) (cancella (x ^ 2) + 2xh + h ^ 2 + cancella (9x) + 9h - cancella (3) - cancella (x ^ 2) - cancella (9x) + cancella (3)) / h #

# = lim_ (h-> 0) (2xh + h ^ 2 + 9h) / h #

# = lim_ (h-> 0) (h (2x + h + 9)) / h #

# = lim_ (h-> 0) (cancel (h) (2x + h + 9)) / cancel (h) #

# = lim_ (h-> 0) 2x + 0 + 9 #

= 2x + 9