MATH 10A Lecture Notes - Lecture 16: Product Rule, Quotient Rule

• School: UCSD
• Department: Mathematics
• Course: MATH 10A
• Professor: Anne Toulson Carter

Document Summary

Example: suppose that v=g(t) represents the volume of water in the pool (in gallons) after t minutes, and h=f(v) represents the depth (in feet) of a pool containing v gallons. Expression: dv dt or g"(t) dh dv or f"(v) Interpretation: rate of change of volume with respect to time (in gallons/min). Interpretation: rate of change of depth with respect to volume (in feet/gallon). Expression: dh dt or (f g)"(t) or d dt. Interpretation: rate of change of depth with respect to time (in ft/min). d dt d dx. [f (g(x ))]= lim b x lim b x lim b x f (g(b)) f (g(x )) b x. [ f (g(b)) f (g(x)) b x f (g(b)) f (g(x )) b x. G(b) g (x) g(b) g (x) g (b) g(x) b x f " (g (x)) g" (x) 4 x2+1 7 z= dz dy y=4 x2+1 z= y7 dz.