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Calculus practice

Power, Constant, and Sum Rules worksheets

Differentiate constants, polynomial sums, reciprocal monomials, and exact rational powers with the original real-domain conditions preserved.

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Differentiate each function with respect to the given variable.

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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 constant, power, and sum rules to exact one-variable functions.

Worked example

Differentiate y = 3x^4 - 2x + 5.

dy/dx = 12x^3 - 2

Differentiate each term independently. The constant term has derivative zero.

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Make the practice count

  • Multiply each coefficient by its exponent.
  • Reduce each nonzero exponent by one.
  • Keep fractional powers exact and preserve domain restrictions.

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Math SheetPower, Constant, and Sum RulesDifferentiate each function with respect to the given variable.1.y =-2·x2.y =-73.y =98·x-754.y =-195.y =x5-1·x4+6·x3+6·x-96.y =-12·x1157.y =-18.y =39.y =-16x10.y =-1720·x-710math-sheet.comPage 1 of 2
Math SheetPower, Constant, and Sum RulesDifferentiate each function with respect to the given variable.11.y =8x312.y =2·x3413.y =1x214.y =-7·x4+7·x3-7·x2-215.y =-7x316.y =-6·x17.y =-175·x-11818.y =-1219.y =x4+2·x3-7·x+720.y =4x3math-sheet.comPage 2 of 2

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