The difference quotient is a formula that finds the average rate of change of any function between two points. In calculus, the difference quotient is the formula used for finding the derivative, which is the limit of the difference quotient between two points as they get closer and closer to each other (this limit is also the rate of change of a function at a single point). The difference quotient was formulated by Isaac Newton.
ð ə WORD_BOUNDARY d ɪ f ɹ ə n s WORD_BOUNDARY k w oʊ ʃ ə n t WORD_BOUNDARY ɪ z WORD_BOUNDARY ʌ WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY ð æ t WORD_BOUNDARY f aɪ n d z WORD_BOUNDARY ð ɪ WORD_BOUNDARY æ v ɹ ɪ d̠ʒ WORD_BOUNDARY ɹ eɪ t WORD_BOUNDARY ʌ v WORD_BOUNDARY t̠ʃ eɪ n d̠ʒ WORD_BOUNDARY ʌ v WORD_BOUNDARY ɛ n i WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY b ɪ t w iː n WORD_BOUNDARY t uː WORD_BOUNDARY p ɔɪ n t s WORD_BOUNDARY ɪ n WORD_BOUNDARY k æ l k j ʊ l ə s WORD_BOUNDARY ð ə WORD_BOUNDARY d ɪ f ɹ ə n s WORD_BOUNDARY k w oʊ ʃ ə n t WORD_BOUNDARY ɪ z WORD_BOUNDARY ð ə WORD_BOUNDARY f ɔ ɹ m j ʊ l ə WORD_BOUNDARY j uː z d WORD_BOUNDARY f ɔ ɹ WORD_BOUNDARY f aɪ n d ɪ ŋ WORD_BOUNDARY ð ə WORD_BOUNDARY d ɪ ɹ ɪ v ə t ɪ v WORD_BOUNDARY w ɪ t̠ʃ WORD_BOUNDARY ɪ z WORD_BOUNDARY ð ə WORD_BOUNDARY l ɪ m ɪ t WORD_BOUNDARY ʌ v ð ə WORD_BOUNDARY d ɪ f ɹ ə n s WORD_BOUNDARY k w oʊ ʃ ə n t WORD_BOUNDARY b ɪ t w iː n WORD_BOUNDARY t uː WORD_BOUNDARY p ɔɪ n t s WORD_BOUNDARY æ z WORD_BOUNDARY ð eɪ WORD_BOUNDARY ɡ ɛ t WORD_BOUNDARY k l oʊ s ə ɹ WORD_BOUNDARY æ n d WORD_BOUNDARY k l oʊ s ə ɹ WORD_BOUNDARY t ʊ WORD_BOUNDARY iː t̠ʃ WORD_BOUNDARY ʌ ð ə ɹ WORD_BOUNDARY ð ɪ s WORD_BOUNDARY l ɪ m ɪ t WORD_BOUNDARY ɪ z WORD_BOUNDARY ɔ l s oʊ WORD_BOUNDARY ð ə WORD_BOUNDARY ɹ eɪ t WORD_BOUNDARY ʌ v WORD_BOUNDARY t̠ʃ eɪ n d̠ʒ WORD_BOUNDARY ə v ə WORD_BOUNDARY f ʌ ŋ k ʃ ə n WORD_BOUNDARY æ t ə WORD_BOUNDARY s ɪ ŋ ɡ ə l WORD_BOUNDARY p ɔɪ n t WORD_BOUNDARY ð ə WORD_BOUNDARY d ɪ f ɹ ə n s WORD_BOUNDARY k w oʊ ʃ ə n t WORD_BOUNDARY w ʌ z WORD_BOUNDARY f ɔ ɹ m j ʊ l eɪ t ɪ d WORD_BOUNDARY b aɪ WORD_BOUNDARY aɪ s ə k WORD_BOUNDARY n uː t ə n WORD_BOUNDARY