MATH 140 Lecture 33: Logarithmic Differentiation

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

Document Summary

The fundamental theorem of calculus states that: G( x)= x a f (t )dt , a x b g"( x)=f (x) if f is continuous on [a, b]. If h and k are differentiable on [a, b], then let: k (x ) G( x)= h( x ) o f (t )dt g" (x)=f (k ( x)) k"( x) f (h( x))h"( x) Quiz 9, problem 2 x ( 8) sin(t 2)dt=(sin( x42))(4 x3)=4 x3 sin x4 d dx . 0 x2 4 0 for [2,3]; x2 4 0 for[0,2] T 5 t 3+1dt: let u=t 3+1 u 1=t 3 du=3t2 dt o. Let r 1: then: xr dx= 1 r+1, if r= 1 , then we have 1 x xr +1+c x 1, refine: g( x)= t. 1 is continuouson(0, ) dx , 1 x dt for x>1 g" ( x)= 1 x.