8868体育

Lesson

Quotient rule

[Formula]

If

飞丑别谤别听u 补苍诲听v are both functions of听x, then

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Example

Differentiate

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Solution

Recall that if where u 补苍诲听v are both functions of听x, then

u = x虏 + 1听 听 听 v = x-1

u' = 2x听 听 听 听 听 听v' = 1

Using this, we get

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Question

Differentiate the function

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Explanation

Use the quotient rule of differentiation, which says that if where u 补苍诲听v are both functions of听x, then

u = x - 2听 听 听 v = (x+1)虏

u' = 1听 听 听 听 听 听v' = 2(x+1)

Using the formula, we have