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Calculus practice

Quotient Rule worksheets

Differentiate exact polynomial quotients in both degree orientations and retain every restriction from the original denominator.

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Differentiate each quotient. Keep the original denominator restriction.

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Practice with exact answers

Keep fractions and rational powers exact. Differentiate the complete original function, then simplify without dropping its domain restrictions.

Learning objective

What this activity builds

Apply the quotient rule to bounded polynomial degree pairs without losing the original domain.

Worked example

Differentiate y = (2x + 1)/(x^2 - 3).

dy/dx = (-2x^2 - 2x - 6)/(x^2 - 3)^2

Use (N'D - ND')/D^2 and retain x^2 - 3 != 0.

Teaching notes

Make the practice count

  • Write N'D - ND' in that order.
  • Square the entire original denominator.
  • Keep the original denominator restriction even when an expression could cancel.

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Polynomial degree pairs
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Math SheetQuotient RuleDifferentiate each quotient. Keep the original denominator restriction.1.y =6·x+4-1·x2+2·x+52.y =6·x2+7·x+8-5·x-63.y =5·x+94·x3+6·x+64.y =-3·x3-5·x2-6·x-4·x-45.y =8·x-4-7·x2-5·x+46.y =-5·x2+4·x-22·x+77.y =8·x+5-2·x3-3·x2+88.y =-5·x3+6·x2+27·x-99.y =-5·x+27·x2+8·x-710.y =-4·x2+3·x-9x+2math-sheet.comPage 1 of 1

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