MATH 140 Lecture Notes - Lecture 8: Power Rule, Differentiable Function, If And Only If

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Denny Gulick

Document Summary

Definition of the derivative f " (a)=lim x a f ( x) f (a) x a =lim h 0 f ( a+h) f (a) h: for a general x in the domain: f (t ) f (x) t x lim t x. If a derivative exists at a, then you say that f is differentiable at a : derivatives can also be written as dy dx , note: f"(a) is the rate of change of f with respect to x at x = a, also, f"(a) is the slope of the line tangent to the graph of f at the point (a, f(a)) Definition: f " ( x)=lim t x f (t ) f (x) t x. Difference of powers: lim t x (t x )(t n 1+t n 2 x+t n 3 x2+t n 2+xn 1) t x. Cancel like terms: lim t x (t n 1+t n 2 x+t n 3 x2+t n 2+xn 1)