Scribe Post from Lucas
Sorry about the lateness of these notes, but the posting thing isn’t working with my account/computer. I am now using Conor’s cumpter. YAYYYYY!!!
Class notes for 11/12
We went over †he curved quiz. See Mrs. Evrard for more personal questions. The multiple choice packet is due on Friday, and the graded hw is due tuesday. On the homework calender it also says that we have a quiz tomorrow. Use the quizzes in my classes to prepare, and also use the derivative plotter on Mrs. Evrard’s homepage. Enjoy.
Product Rule
d(uv)=u’v+uv’
This can also be written with g(x) and h(x)
Quotient Rule
d(u/v)=(u’v-uv’)/(v^2)
d((8x+1)^6/(5x+2)^9)=
(6(8x+1)^5 * (8) * (5x+2)^9 – (8x+1)^6 * (5x+2)^9 * 9) / ((5x+2)^9)^2
d((8x+1)^6/(5x+2)^9)=
(3) * (8x+1)^5 * (5x+2)^8 [(16) * (5x+2) - (15) * (8x+1)] / (5x+2)^18
d((8x+1)^6/(5x+2)^9)=
(3) * (8x+1)^5 * [(16) * (5x+2) - (15) * (8x+1)] / (5x+2)^10
When the numerator is constant, it’s easiest not to use the quotient rule, because
1000/(3-t)=1000(3-t)^-1
Using the quotient rule to solve for the derivative of tan x
sin x/ cos x
d(sin x/ cos x)= (cos x*cos x – sin x * sin x) / (cos^2 x)
d(sin x/ cos x)= (cos^2 x)^-1 = sec^2 x
