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Quotient Rule Notes

Quotient Rule Notes. The following are examples of quotients:. (a). (b). (c). (d). (c) can be divided out to form a simple function as there is a single polynomial term in the denominator. For the others we use the quotient rule. SUMMARY. To differentiate a quotient:.

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Quotient Rule Notes

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  1. Quotient Rule Notes

  2. The following are examples of quotients: (a) (b) (c) (d) (c) can be divided out to form a simple function as there is a single polynomial term in the denominator. For the others we use the quotient rule.

  3. SUMMARY To differentiate a quotient: • Check if it is possible to divide out. If so, do it and differentiate each term. • Otherwise use the quotient rule: where u and v are both functions of x If ,

  4. e.g. 1 Differentiate to find . Solution: We now need to simplify.

  5. We could simplify the numerator by taking out the common factor x, but it’s easier to multiply out the brackets. We don’t touch the denominator. Multiplying out numerator: Now collect like terms: and factorise: We leave the brackets in the denominator. ( A factorised form is considered to be simpler. )

  6. We can now differentiate the trig function by writing

  7. So, This answer can be simplified: Also, is defined as So,

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