Grade 12 · Math · Calculus

12th grade The chain rule worksheet

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The chain rule

Grade 12 Math Worksheet - Building Confidence

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Ari uses the chain rule on h(x) = (3x − 4)⁴. What is h′(1)?
Esme uses the chain rule on h(x) = (3x − 4)³. What is h′(2)?
Jun uses the chain rule on h(x) = (-2x + 7)³. What is h′(2)?
At x = 1, 3, 2, 5; at x = 3, 0, 1, -4. Kira uses the table shown. If h(x) = f(g(x)), what is h′(1)?
At x = 2, -1, 3, 4; at x = -1, 5, 0, 2. Luz uses the table shown. If h(x) = f(g(x)), what is h′(2)?
At x = 0, 4, -2, 7; at x = 4, 1, 3, 5. Milo uses the table shown. If h(x) = f(g(x)), what is h′(0)?
At x = 3, 2, 4, -1; at x = 2, 6, 1, 3. Noah uses the table shown. If h(x) = f(g(x)), what is h′(3)?
8.
Pia names the inside u = x² + 5 and uses the chain rule on h(x) = (x² + 5)³. Which is h′(x)?
- h′(x) = 6x(x² + 5)²
- h′(x) = 6x(x² + 5)³
- h′(x) = 3(2x)²
- h′(x) = 3(x² + 5)²
9.
Ren names the inside u = 4x − 1 and uses the chain rule on h(x) = (4x − 1)⁵. Which is h′(x)?
- h′(x) = 20(4x − 1)⁵
- h′(x) = 5(4x − 1)⁴
- h′(x) = 20(4x − 1)⁴
- h′(x) = 5 × 4⁴
10.
Tala names the inside u = x² + 9 and uses the chain rule on h(x) = √(x² + 9). Which is h′(x)?
- h′(x) = 1/(2√(x² + 9))
- h′(x) = x/√(x² + 9)
- h′(x) = x√(x² + 9)
- h′(x) = 1/(2√(2x))

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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