### SOLUTIONS TO DIFFERENTIATION OF FUNCTIONS USING THE QUOTIENT RULE

SOLUTION 1 : Differentiate .

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 2x 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.)

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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 2x and from inside the brackets.)

(Factor , and from the numerator.)

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