3.4, #8, Given Problem.
 

Differentiate:	3.4, #8, Given Problem.
	Here we first apply the quotient rule.
	Here we apply our new rules for differentiating the sin and cosine.
	Algebraic simplification. (Multiply out the quantities in the numerator)
	Here we make a substitution based on the fact that . (Pythagorean Identity)
	Cancellation of the numerator with one of the two identical factors in the denominator. We have our derivative.

3.4, #14, Given Problem.
 

	3.4, #14, Given Problem.
	Here we use one of the trigonometric reciprocal identities to write the sec(x) as .
	Now we apply the quotient rule.
	Note that the derivative of 1 is zero and the first product in the numerator becomes zero. In the second part of the numerator, the derivative of the cosine is - sin x, so this becomes sin x.
	Here we factor the fraction into two parts.
	Then, once again we use trigonometric identities to make substitutions. In the first fraction we use a reciprocal identity, and in the second fraction we substitute based on a ratio identity.

3.4, #34, Given Problem.
 

Find the given derivative by finding the first few  derivativesand observing the pattern that occurs:	3.4, #34, Given Problem. This is asking us to find the 35th derivative of the quantity by doing some derivatives and observing any patterns.
	We calculate the first derivative. Note, that in the first portion of this derivative we have to use the product rule.
	Here we calculate the second derivative. Watch carefully how the signs are affected. We gather like terms to get a final result.
	In the third derivative we continue using the product rule on the first portion of the derivative. We are trying to observe any patterns in our results.
	We should be noticing that the coefficient on the last part of every answer is equal to the degree of the derivative we are finding.
	We also notice that the first part of the answer is always one of four choices:  in that order. (a series of 4 choices)
	We also notice that the last term of each answer also has a sequence of 4 possible choices (disregarding the coefficients which we already found a pattern for):  in that order.
	And so we apply all of patterns to get this answer.

	Assignment
1-37. Odds
Lesson 3.4, Pages 223-225