CAS MA 123 Lecture Notes - Lecture 14: Irix

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 123
• Professor: John Bergdall

Document Summary

Ma123 lecture 14 derivatives of logarithms. Remember if b > 0 function as x approaches bx defined on whole real line x in (- , ) B=e=2. 72828 is distinguished by the property that the slope of the tangent line y=bx @ x=0 is. The function ex is 1-1 i. e. ex = ex" x=x" thus ex has an infinite function ln(x) called the natural logarithm. The same is true for all base b, the corresponding inverse is written as logb(x). (b=e logex = lnx) The defining property of lnx is elnx=x where x>0. Suppose f(x) is a function and it has an inverse function f-1(x) (x0,y0) is on the graph of f(x) f(x0)= y0. Graph of f-1(x) = reflection of graph of f(x) around the lim y=x! Thus because ex is 1-1 >>> ln(x,x) = ln(x) + ln(x) Y=ln(x) is defined on x>0 implicitly by the equation ey=x. If you differentiate each side of ey=x you get dy/dx = 1/x.