Grade 12 · Math · Calculus

12th grade The chain rule worksheet

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The chain rule

Grade 12 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Ari uses the chain rule on h(x) = √(3x + 1). What is h′(5)?
Bo uses the chain rule on h(x) = √(2x + 5). What is h′(2)?
Esme uses the chain rule on h(x) = √(5x − 1). What is h′(2)?
Jun uses the chain rule on h(x) = √(4x + 9). What is h′(4)?
Kira writes h(x) = 6/(2x − 1)² as 6(2x − 1)⁻² and uses the chain rule. What is h′(1)?
Luz writes h(x) = 8/(3x + 1)² as 8(3x + 1)⁻² and uses the chain rule. What is h′(1)?
Milo writes h(x) = 5/(2x + 1)³ as 5(2x + 1)⁻³ and uses the chain rule. What is h′(-1)?
Noah writes h(x) = 9/(-2x + 5)² as 9(-2x + 5)⁻² and uses the chain rule. What is h′(1)?
f(x) = x³ + 2x and g(x) = x² − 1. Pia differentiates h(x) = f(g(x)). What is h′(2)?
f(x) = x³ + 3x and g(x) = x² − 4. Zee differentiates h(x) = f(g(x)). What is h′(3)?

The chain rule. Every version has 10 questions, and the answer key prints on the second page.

I can find the inside and outside of a composite and use the chain rule.
I can use the chain rule from a table of values.
I can combine the chain rule with the product rule and with roots and negative powers.

Standard: none (beyond CCSS)

composite: A function inside another: f(g(x)).

inside, outside: In f(g(x)), g is inside and f is outside.

chain rule: (f(g(x)))′ = f′(g(x)) × g′(x).

Used the outside derivative but did not multiply by the inside's derivative. The chain rule is outside′(inside) × inside′.

Multiplied by the inside's derivative but did not lower the outside power by 1.

Swapped the inside for its derivative. The inside stays; its derivative multiplies.

What is the most common mistake with the chain rule?

Used the outside derivative but did not multiply by the inside's derivative. The chain rule is outside′(inside) × inside′.

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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