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Calculus practice

Chain Rule worksheets

Differentiate exact powers of polynomial binomials and square roots of odd polynomial powers, keeping each answer in concise factored form.

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Differentiate each function. Give each answer in concise factored form.

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Keep the structure visible

Differentiate the outer power, multiply by the inner derivative, and keep the original polynomial factor unexpanded. Radical questions retain the square root in the final answer.

Learning objective

What this activity builds

Apply the chain rule to a bounded family of power and radical composites with exact coefficients.

Worked example

Differentiate y = 3(5x^3 + 4x)^4.

dy/dx = (180x^2 + 48)(5x^3 + 4x)^3

Multiply by the outer power, reduce that power by one, then multiply by the derivative of the inner polynomial.

Teaching notes

Make the practice count

  • Differentiate the outside while keeping the inside unchanged.
  • Multiply by the derivative of the inner polynomial.
  • Keep exact fractional coefficients and leave the final answer factored.

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Math SheetChain RuleDifferentiate each function. Give each answer in concise factored form.1.y =-32·2·x-532.y =-23·-4·x2-6·x43.y =32·x3-5·x254.y =-3·-4·x-365.y =-1·4·x2+636.y =-12·x3+7·x247.y =2·2·x+558.y =12·-4·x2+5·x69.y =23·-4·x3+7·x2310.y =5·x-24math-sheet.comPage 1 of 1

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