Download derivatives of e day 1(5.4)

CALCULUS – SEC. 5.4

Review logarithms, derivatives of natural logs, and learn and apply the rules for derivatives
of y  e x
REVIEW #1 Rewrite into exponential form:
log3 81  4
REVIEW #2 Rewrite using rules for logarithms
( +, -, exponent rule)
 x  x2  5 
ln 



y


REVIEW #3
Solve for x; round to three decimal places, please.
54 x  670
REVIEW #4
Find the derivative:
y  ln  5 x 2  3
SECTION 5.4 – Derivatives involving y  e x
Type into your calculator:
Which represents
Y1  (1  1 / x)  x
 1
y  1  
x

x
Go to TABLE and continue scrolling “to infinity”. What value is this function
approaching? ______________________________
x
 1
So, lim 1    ________
x 
x

THIS IS ONE OF THE EASIEST DERIVATIVE RULES YOU WILL LEARN!!
y  e x then y '  _____________
EX. 1
but y  e f ( x ) then y '  _____________
y  e5x
EX. 2
y  e4x
EX. 3
y  ln  e 2 x  4 x 
EX. 4
 e2 x 
y  ln  2 x

 e 1
2
EX. 5
e2 x
y  2x
e 1
EX. 6
y  2 x  e4 x
(NOT the same as EX. 4!)