Reflection 10/10

This week in calculus we did more on the chain rule and reviewed for the exam. The chain rule, in words, is you take the derivative of the outside, recopy the inside, then multiply by the derivative of the inside. "Outside"= y=f(u) "Inside"= u=...

Examples:

y= 1/x+1

outside= y=1/u
inside= u=x+1


y=sin(2x)

outside= y=sin(u)
inside= u=2x


y=sqrt3x^2-x+1

outside= y=sqrt(u)
inside= u=3x^2-x+1
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d/dx (x^2 + 1)^3

outside= y=u^3
inside= u=x^2 + 1


3u^2 (2x)
3(x^2+1)(2x)
=6x(x^2+1)^2

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Problem with the chain rule and the quotient rule. You have to find which rule is inside of the other.

Example:

d/dx -7/(2t-3)^2

1. Quotient Rule
2. Chain Rule


(2t-3)^2(0) - [(-7)(2(2t-3)^1(2)/(2t-3)^4

28(2t-3)/(2t-3)^4
28/(2t-3)^3
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SO that pretty much sums up this week, EXAAAAAMMMM tomorrrroww! Study study study, lets all get A's.