MATH-UA 211 Lecture 12: Derivatives of Logs and Exponentials, Implicit Differentiation

• School: New York University
• Department: Math
• Course: MATH-UA 211
• Professor: Majmudar

Document Summary

Math- ua 211- lecture 12- exponentials, log function derivatives, implicit. A x a y=ay+x ax ay =ax y (ax)y=ax y d dx ax=ax ln(a) d dx. 2x=2x ln2 o d dx au=au ln (a) du dx d dx d dx d dx. Ex2 2x o o o o d dx ln x= 1 x d dx log a( x)= 1 x ln a: chain rule: Du dx ln u= ln x4= 1 x4 4 x3 d dx d dx o o: y" x ln(ln ) = = x y o o: find an equation of tangent at x=3 dy dx, x=3 where y=4, at (3,4) 4 ( x 3) o x3+ y3=6xy, find y" d dx (x3+ y3)= d dx (6xy) 3 x2+3 y2( dy dx)=6y+6x( dy dx) 3 y2( dy dx) 6x( dy dx)=6y 3x2 dy dx (3 y2 6x)=6y 3x2 6y 3 x2.