Third Holiday Reflection

My third and final blog of the holiday
will refer to chapter 5 that has to do with logs.

here is a few examples of what we learned in
this chapter:

ln x^2y/10 EXPAND

ln x^2+ ln y- ln 10

2lnx+lny-ln10


ln eyz^2/g EXPAND

lne+lny+2lnz-lng

1+lny+2lnz-lng


3ln(x+2)-ln(x-1)

=ln(x+2)^3/(x-1)


Derivative of a natural log:

d/dx lnu= 1/u x du

examples:

d/dx ln2x= 1/2x x 2= 1/x

d/dx ln(x^2+1)=1/x^2+1 x 2x= 2x/ x^2+1

d/dx xlnx= x(1/x x 1) +lnx(1)=1+lnx

d/dx lnx^3= 1/x^3 x 3x^2= 3/x

d/dx (lnx)^3= 3(lnx)^2 x 1/x x 1=

3(lnx)^2/x


that is all!
i hope everyone has
a good christmas and new years!