Then

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* SOLUTION 2 :* Differentiate .

Then

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* SOLUTION 3 :* Differentiate .

Then

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* SOLUTION 4 :* Differentiate .

Then

(Recall the well-known trigonometry identity .)

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* SOLUTION 5 :* Differentiate .

Then

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* SOLUTION 6 :* Differentiate .

Then

(Begin to simplify the final answer by getting a common denominator in the numerator.)

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* SOLUTION 7 :* Differentiate .

Then

(Recall that .)

(Recall that and .)

(Recall that .)

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* SOLUTION 8 :* Differentiate .

Then

(Factor 2*x* and from the numerator.)

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* SOLUTION 9 :* Consider the function . Evaluate .
Use the quotient rule to find the derivative of *f* . Then

(Recall that and .)

(Factor from the numerator.)

.

Finally,

(Recall that and .)

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* SOLUTION 10 :* Differentiate . Apply
the quotient rule first. Then

(Apply the product rule in the first part of the numerator.)

(Factor from inside the brackets.)

(Now factor from the numerator.)

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* SOLUTION 11 :* Differentiate . Apply the quotient rule first. Then

(Now apply the product rule in the first part of the numerator.)

(Factor 2*x* and from inside the brackets.)

(Factor , and from the numerator.)

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Wed Jul 30 20:10:53 PDT 1997