Calculus 1000A/B Lecture Notes - Lecture 9: Product Rule, 32X, Quotient Rule

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Pei Yu

Document Summary

2. 8 (cont"d) suppose f (x) is de ned at x = a and near a. The derivative of f at a is f (a) = df dx(cid:12)(cid:12)(cid:12)x=a lim h 0. = f (x)(cid:12)(cid:12)(cid:12)x=a f (a + h) f (a) d dx f (x)(cid:12)(cid:12)(cid:12)x=a h lim x a f (x) f (a) x a. = the slope of the tangent line to the graph of y = f (x) at x = a. = the slope of the tangent line to the graph of y = f (x) at (a, f (a)) = the rate of change of f (x) at x = a. From the de nition if follows immediately: if f (a) and g (a) are de ned, then (f + g) (a) = f (a) + g (a). Accurate justi cation: f (a) and g (a) are de ned means that the limits lim h 0 f (a+h) f (a) h.