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Calculus Chapter 3 Review (Derivative Rules (Product, Quotient, Sub, Add,…
Calculus Chapter 3 Review
Limit / x-a
lim h > 0 f(x+h) - f(x) / h
Make sure you write "lim h > o" on EVERY step
Don't forget about parentheses
1/x^2
(1/(x+h)^2 - 1/x^2 ) / h, solve to get h out of a denominator
Multiply to get a common denominator over h
Solve until h is out of the denominator, then let h go to where it approaches
f(x) = 3 / x-2
(3/x-2) - (3/a-2) / (x-a)
Never forget the lim x > a
Same process, you just have a
-3/(a-2)^2
If you're factoring and need to change the order, take out a negative factor
Y = x^3 - 1, find average rate of change of y
We want average derivatives/rate of change
f(b) - f(a)/b-a
(3^2 -1) - ((-2)^3-1) / 3-(-2) = 27 - 1 - (-8 - 1) /( 3 + 2)
35/5 = 7
Given table, approximate derivative
Slope at a value
Take your values and take a slope from there :/
Try to use the values that are just outside of the wanted point
Tangent lines/Definitions as piecewise
Take derivative and use point slope
Piecewise
Derivative Rules
Product
Quotient
Sub
Add
Chain
Power