Grade 12 · Math · Calculus

12th grade Product and quotient rules worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Product and quotient rules

Grade 12 Math Worksheet - Building Confidence

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f = 4, f′ = -1, g = 3, g′ = 6. Bo uses the values shown and the product rule. If h(x) = f(x)g(x), what is h′(2)?
f = -2, f′ = 3, g = 5, g′ = 4. Esme uses the values shown and the product rule. If h(x) = f(x)g(x), what is h′(-1)?
f = 6, f′ = 5, g = -2, g′ = 3. Jun uses the values shown and the product rule. If h(x) = f(x)g(x), what is h′(3)?
f = 6, f′ = 1, g = 2, g′ = 3. Kira uses the values shown and the quotient rule. If h(x) = f(x)/g(x), what is h′(1)?
f = 8, f′ = 0, g = 4, g′ = 2. Milo uses the values shown and the quotient rule. If h(x) = f(x)/g(x), what is h′(0)?
f = 2, f′ = 5, g = 3, g′ = -1. Noah uses the values shown and the quotient rule. If h(x) = f(x)/g(x), what is h′(3)?
Pia uses the product rule on h(x) = (x² + 1)(3x − 2), without expanding. What is h′(2)?
Ren uses the product rule on h(x) = (x² + 3)(2x + 5), without expanding. What is h′(1)?
Tala uses the product rule on h(x) = (x² − 4)(5x + 1), without expanding. What is h′(3)?
Zee uses the product rule on h(x) = (x² + 2)(-3x + 6), without expanding. What is h′(-2)?

The product and quotient rules. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

product rule: (fg)′ = f′g + fg′.

quotient rule: (f/g)′ = (f′g − fg′)/g².

revenue: Price times number sold.

Multiplied the two derivatives. The product rule is f′g + fg′: one factor changes at a time.

Used only one part of the product rule. Each factor's change adds its own term.

Subtracted the quotient rule's top in the wrong order, so the sign flipped. The top is f′g − fg′.

What is the most common mistake with product and quotient rules?

Multiplied the two derivatives. The product rule is f′g + fg′: one factor changes at a time.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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